02341_02431_20341_20431_23041
Counting sequence:
1, 1, 2, 6, 24, 115, 614, 3504, 20885, 128292, 805653, 5145429, 33303599, 217908781, 1438724862, 9571907890, 64101679227, 431736779901, 2922449260601, 19870384374339, 135641064945713, 929240910500579, 6386603302226684, 44023956710482330, 304281593265160497, 2108306372658500908, 14641271983684948936, 101891127272240583862, 710460827935633351673, 4962847842292055280159, 34726081323945323257852, 243369870581272537634828, 1708129797304985717387885, 12005459038609995833694929, 84489911897605221699486500, 595342075793252768288493694, 4199853386788803485520836431, 29660615540345068794061072896, 209690856811649720554969284270, 1483914625019128791358683978884, 10511070724524819258146599088440, 74520153422794373693400942243514, 528774868262578531523892021124834, 3755095545889000304616460444568088, 26687525673866155672433935803770268, 189809454428188501933013280325376147, 1350938686994473589798643322731872894, 9621629950820172901656730176426908846, 68571655760634842582733173114079328694, 489003659657078160600474562096267970101, 3489315739574008146588344423833012551087, 24912594062930806323511796803719859487893, 177966629698290257265458493872775542455187, 1272008766810252555790503039331313768437318, 9096304711031514816770277318433069566641166, 65081145716526913705034507648326183604752304, 465857436368946284747851516994186600083314050, 3336193926038315050454263318322033727309519351, 23902486822246007998320346662763857478462487188, 171325462747608776816169032121733326882121288682, 1228518133256716043582894542727952249646937578065, 8812845763567082133218384746467549572478332938255, 63244112334153007931068303247942859445189892382720, 454033634052676934103664973001217568453670200728740, 3260730089321017783053273761179414710940612995467863, 23425869479590318337431680140034863394589310832297765, 168354989638325608101167693314130120875303263506253804, 1210322868730434220667177372118082671360315727245246340, 8703966748602328373022471175384596308805668938690241220, 62613775398090265586022846278585135927224678261549906371, 450562831396326772582586176252705033473777736819900856116, 3243171536025757989386867510354998254144830125114815129136, 23351242841199258017116362035346782132214558423529360088108, 168179162956505174798609562929430346358630870167209332196789, 1211583078598267269234471606898455251174256151066068388261649, 8730716556441988339629123452702464592355792301542141281679865, 62930217226422520831721140093849284110219487919917677792341527, 453709963706251569334056657347518151761428924128380606451898342, 3271932607082142962242010158288171171135645201956069150816889008, 23601230104335241313049865872724176408507961880873095661399659226, 170281157658046111942261563095026329775480796673667926985391639773, 1228846733632501145371255292469791808803302120406934878186101589082, 8870040665081389611843195383678671997605657742945026909807866605122, 64039502671125478548964717795430769832384782865242272419944665235200, 462447571269305322870201679368102570552602403316603829496688761631109, 3340158770610532165638516822035937572364975643238407687754077580173080, 24130131721197429999698029857609825325443619360572482176243079816873490, 174356538003602882099757936633413827186686197859251122129886556523364302, 1260087786149877984129498120911522188943551003213041736514908284783169329, 9108471629359207323312954540895610835454157846903541322961272697536644070, 65852239013734417943094185504728354080714487284833242692195420340679592049, 476183293078728432747431451482372949757466319453196139018775102608744699345, 3443932542612124766171818784343285949407706190244590159571665944630969234325, 24912100548976588098934947414117350077673315009889451256725349805520150298797, 180235235341039847591705093449768948414156325495183429923882155047070700618860, 1304190834961215722947928532753240738541497730838561324101028673656088905886972, 9438721939677110969636535732569706930196209057096939176431890663676980003213838, 68321028373485482099480025044438241247567484513886756528381612633452110966752460, 494610518515176478546167025544303483111311203529328913901225191734567173448545879, 3581283404716153573506465391483280404047375729899793108404751299597529631835861935, 25934572936432267692353316346037543817920404993745926918264156597412602215630859209
Implicit equation for the generating function in Maple syntax:
x^4*(x^2-3*x+1)*F(x)^5-x^3*(9*x^2-19*x+6)*F(x)^4+(2*x^5+8*x^4-27*x^3+5*x^2+4*x-1)*F(x)^3+(-15*x^4+20*x^3+23*x^2-21*x+4)*F(x)^2+(x^4+11*x^3-43*x^2+28*x-5)*F(x)-(3*x-2)*(2*x^2-4*x+1) = 0
Implicit equation for the generating function in latex syntax:
x^{4} \left(x^{2}-3 x +1\right) F \! \left(x \right)^{5}-x^{3} \left(9 x^{2}-19 x +6\right) F \! \left(x \right)^{4}+\left(2 x^{5}+8 x^{4}-27 x^{3}+5 x^{2}+4 x -1\right) F \! \left(x \right)^{3}+\left(-15 x^{4}+20 x^{3}+23 x^{2}-21 x +4\right) F \! \left(x \right)^{2}+\left(x^{4}+11 x^{3}-43 x^{2}+28 x -5\right) F \! \left(x \right)-\left(3 x -2\right) \left(2 x^{2}-4 x +1\right) = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 115
a(6) = 614
a(7) = 3504
a(8) = 20885
a(9) = 128292
a(10) = 805653
a(11) = 5145429
a(12) = 33303599
a(13) = 217908781
a(14) = 1438724862
a(15) = 9571907890
a(16) = 64101679227
a(17) = 431736779901
a(18) = 2922449260601
a(19) = 19870384374339
a(20) = 135641064945713
a(21) = 929240910500579
a(22) = 6386603302226684
a(23) = 44023956710482330
a(24) = 304281593265160497
a(25) = 2108306372658500908
a(26) = 14641271983684948936
a(27) = 101891127272240583862
a(28) = 710460827935633351673
a(29) = 4962847842292055280159
a(30) = 34726081323945323257852
a(31) = 243369870581272537634828
a(32) = 1708129797304985717387885
a(33) = 12005459038609995833694929
a(34) = 84489911897605221699486500
a(35) = 595342075793252768288493694
a(36) = 4199853386788803485520836431
a(37) = 29660615540345068794061072896
a(38) = 209690856811649720554969284270
a(39) = 1483914625019128791358683978884
a(40) = 10511070724524819258146599088440
a(41) = 74520153422794373693400942243514
a(42) = 528774868262578531523892021124834
a(43) = 3755095545889000304616460444568088
a(44) = 26687525673866155672433935803770268
a(45) = 189809454428188501933013280325376147
a(46) = 1350938686994473589798643322731872894
a(47) = 9621629950820172901656730176426908846
a(48) = 68571655760634842582733173114079328694
a(49) = 489003659657078160600474562096267970101
a(50) = 3489315739574008146588344423833012551087
a(51) = 24912594062930806323511796803719859487893
a(52) = 177966629698290257265458493872775542455187
a(53) = 1272008766810252555790503039331313768437318
a(54) = 9096304711031514816770277318433069566641166
a(55) = 65081145716526913705034507648326183604752304
a(56) = 465857436368946284747851516994186600083314050
a(57) = 3336193926038315050454263318322033727309519351
a(58) = 23902486822246007998320346662763857478462487188
a(59) = 171325462747608776816169032121733326882121288682
a(60) = 1228518133256716043582894542727952249646937578065
a(61) = 8812845763567082133218384746467549572478332938255
a(62) = 63244112334153007931068303247942859445189892382720
a(63) = 454033634052676934103664973001217568453670200728740
a(64) = 3260730089321017783053273761179414710940612995467863
a(65) = 23425869479590318337431680140034863394589310832297765
a(66) = 168354989638325608101167693314130120875303263506253804
a(67) = 1210322868730434220667177372118082671360315727245246340
a(68) = 8703966748602328373022471175384596308805668938690241220
a(n+69) = -1/24*(153413*n^3+30726732*n^2+2051154163*n+45636029460)/(n+70)/(n+67)/(n+71)*a(n+67)+1/2*(235*n^2+31516*n+1056496)/(n+71)/(n+67)*a(n+68)-2145/16*(2*n+3)*(2*n+1)*(n+2)*(n+1)/(n+70)/(n+69)/(n+67)/(n+71)*a(n)+1/768*(3297773237259923850*n^4+745303932617683742653*n^3+63131736449977288562571*n^2+2375445868049650632661790*n+33499199250123676293923892)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+57)-1/768*(436021605335092969*n^4+100508951608476694437*n^3+8684777917886067646475*n^2+333391482428163369449313*n+4797381987945343479598080)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+58)+1/1536*(91086851275342523*n^4+21372526156688262478*n^3+1879880240350856484919*n^2+73462209636814753699148*n+1076143713700403798333856)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+59)-1/1536*(7402619901340187*n^4+1765011447347501652*n^3+157752115783553661817*n^2+6264022113223606067256*n+93238287258855218336772)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+60)+1/768*(218281568683475*n^4+52743736012696770*n^3+4776805995524500777*n^2+192176032859293427112*n+2897778994758860030982)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+61)-1/768*(7009233775961*n^4+1696784831262837*n^3+153827794085358334*n^2+6189362013836940990*n+93247058079870094764)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+62)-1/768*(206863224248*n^4+54992295822609*n^3+5472098351940862*n^2+241590799540141443*n+3993407830929459126)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+63)+1/384*(23235886495*n^4+6029880561167*n^3+586745940934688*n^2+25372841278736920*n+411413935531691376)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+64)-1/384*(1737288148*n^4+455387357667*n^3+44759140396994*n^2+1955061269811405*n+32020688007132954)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+65)+1/192*(40402187*n^4+10729982198*n^3+1068504707581*n^2+47285000606938*n+784609684430016)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+66)+1/1536*(1346244465440653430663463*n^4+276519885050316744899319914*n^3+21315720693393827204346233127*n^2+730855043580593155233567508228*n+9404439156471865731631516936680)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+50)-1/768*(138668549985878719425449*n^4+29138976566398334202079068*n^3+2297344444000507054456800457*n^2+80541087316298781178831950288*n+1059398952063320394836714213274)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+51)+1/1536*(42385912053065919534199*n^4+9152326979000713434379432*n^3+741223302992689579938137855*n^2+26684362138407435502633824842*n+360300637249061738797934958096)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+52)-1/768*(1971059264981038690359*n^4+446426083033959255727855*n^3+37853327346224445331390767*n^2+1424306180392529027160116003*n+20068240053619060452317279760)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+53)-1/1024*(91749947722823911371*n^4+14190648596863478647338*n^3+675441576831345042441381*n^2+6582776975828857032150702*n-159758798404967841515864744)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+54)+1/1536*(152218632569691298115*n^4+32394201545327128853832*n^3+2578532550279009457177921*n^2+90961165397446036583550264*n+1199493508504786268652583884)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+55)-1/3072*(76808308241162490495*n^4+16953174586251190235578*n^3+1401952096572971109836325*n^2+51478198556222870645091650*n+708135552306043077943090968)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+56)-1/384*(1641786441114063188318987711*n^4+295582175485002365766743047010*n^3+19938935012288379294329714712583*n^2+597263189039959938322631050369336*n+6703079484537241412642815439511297)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+44)+1/768*(709763180751513107925949002*n^4+130521848228277050490392575061*n^3+8989616094463547913404417028567*n^2+274826730727480146733939644890104*n+3146545883550275627256575964126210)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+45)-1/3072*(426368762686738385856868043*n^4+79962053782487559764511955834*n^3+5610078521066060508405563446909*n^2+174497166493236758823508010615318*n+2030063323590418217385920210630784)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+46)+1/768*(1865706855020779402988606*n^4+337619766548255929754887401*n^3+21916814847860438564820349849*n^2+595062656304366902736826663278*n+5500972362511773333660589940712)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+47)+1/3072*(22658408003102384695413369*n^4+4471916314078392263455920242*n^3+331832380923228756606123476655*n^2+10971972617920553668403354537326*n+136392186774435429109246503322296)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+48)-1/768*(2445116652422354506802171*n^4+491790316042958704462705982*n^3+37138827745920936521504976115*n^2+1248049798566496653796558550536*n+15747221141753126004219370652640)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+49)-1/768*(1289800930694240884846804344209*n^4+201958915933780294727320648725862*n^3+11855172231669781206149856250112878*n^2+309202142536102159985538711983095715*n+3023290014942033819053172823256178006)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+38)+1/1536*(1270438242868496944349248752703*n^4+203892293485622584685653035762990*n^3+12266946968476764965229707421598049*n^2+327903039326548960384502571888116274*n+3285792298916521849226818965938737824)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+39)-1/1536*(563988132692675320070057095021*n^4+92719561424331622999309619891786*n^3+5714009004689790820575385885593593*n^2+156445435131672996163407636366974728*n+1605643459925282062618422373485556260)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+40)+1/1536*(224501774614696983138176899735*n^4+37786307042831947076495909823758*n^3+2383914578623164744910525310686649*n^2+66814696458247534467322801837611226*n+701922836420470335439027649407873788)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+41)-1/1536*(79477940597878402843018610261*n^4+13688083847262389209385568137072*n^3+883575481330240066707419889413683*n^2+25335648111729962276944260767226700*n+272281138248748951425933934291723788)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+42)+1/768*(12344385918221301341630451622*n^4+2174294477931303696994658342770*n^3+143521873227747080531774449661567*n^2+4207745421425345651510894963773097*n+46229632279516446561208378869002496)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+43)-1/3072*(46337294869700488078397754611923*n^4+6168701371664858309379022915371518*n^3+307907892955331938382140576742105933*n^2+6829643069319863263530011844207377914*n+56798785261461265829554496987613230856)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+32)+1/1536*(20430733537045546383566237554539*n^4+2799886232139713160089368306775546*n^3+143864049856553224602272122787696145*n^2+3284776634229296888020743180445967326*n+28119972833901870703643271321371373804)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+33)-1/768*(8185913756073408436673452250954*n^4+1153837941022339269851644855809626*n^3+60977495104996851836106247879804627*n^2+1431949282834147287842232675094288099*n+12607610838737263039674935774691407598)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+34)+1/512*(3974169156407476918709795945657*n^4+575706214060082561397617074337284*n^3+31267549962569425856578974152283531*n^2+754590322553815116288148977901799172*n+6827579385663410890567351931477081656)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+35)-1/768*(3944012103520209303656419233028*n^4+586744535212034533499156852189471*n^3+32725672925805441044881377108522074*n^2+811040856803020551139033046141304307*n+7535724535547288834342448419118101592)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+36)+1/1536*(4737677638289416679609595343639*n^4+723323033488004628459167356203148*n^3+41401561407640373198093120710987865*n^2+1052941935996603425438145037552967936*n+10039420770762418702116379209933698484)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+37)+1/512*(3402640943970975497549036173923*n^4+385555204028835431861658800199518*n^3+16383140264649935630477470661481341*n^2+309407530310646320020222714463550082*n+2191282993015071755525484737032145600)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+27)-1/768*(7301676348292086109783244707997*n^4+856663703648890593982996219573718*n^3+37689007439533836438217876937570386*n^2+736918881709161972639641978036471845*n+5403026605242558270299664650739738612)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+28)+1/768*(9478096638003299160009932781277*n^4+1149746230092757574052210483332420*n^3+52297548122479333106091332009680949*n^2+1057168133622924071463386008859046136*n+8013141247760999226696287731400912514)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+29)-1/3072*(44653728311574386136752137167319*n^4+5593422808232503654088888712253922*n^3+262713323334424520517769797594827201*n^2+5483484044883268392775177044148525798*n+42915509512304167190972929140634305144)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+30)+1/768*(11933911136070629195402527182599*n^4+1541867740313376804304781300837652*n^3+74693850064294164013869533490733426*n^2+1607984502759780705544117957140858435*n+12979312748452685168830805540310434580)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+31)+1/1536*(160793411296706179038204237099*n^4+14222881860468674413064202365404*n^3+472037463901508561915331401618463*n^2+6966469444609884182605407340743242*n+38574590799811433598159726020865840)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+21)-1/3072*(814511191584175713394865290077*n^4+75455669155327180869380726928698*n^3+2622539999086509128251392003222915*n^2+40528964752403857208176807546483918*n+234977891025247448115079045935867384)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+22)+1/768*(468109857861216042447835020884*n^4+45329510977577195286365832659110*n^3+1646677346298972645268303017243583*n^2+26595505822747774547527751925679217*n+161133460941834019776338107882405332)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+23)-1/3072*(3918906120140980926086415671449*n^4+395867848982142605097208346494762*n^3+14999801843459566246108344690733607*n^2+252667670344546497011605589433329222*n+1596427556260048464432248411694546264)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+24)+1/1536*(3734994513176976837276237801845*n^4+392766533725825581537902205251356*n^3+15491248508710996034368868980739449*n^2+271597683532428578663848817645788502*n+1785917182541769787235328760548711108)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+25)-1/1536*(6477528922882912454602034951163*n^4+707716099098347993196622776029840*n^3+28998741186452751910194301457314317*n^2+528142681527488848118232697442650156*n+3607321251397618916991065859636119880)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+26)+1/768*(21068231881131528479674309*n^4+1348135379299291062799367623*n^3+32396802315192558565719149297*n^2+346498340861416037242538295743*n+1391622802111359221531063027316)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+15)-1/768*(123569104538644310114470026*n^4+8416101533075995817586444593*n^3+215185680204527765972857584561*n^2+2447869308255199158750396871750*n+10452784915940647484121485217510)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+16)+1/1536*(1213142275404096173535906245*n^4+87526676820894000217643499232*n^3+2370150458974274731882004258791*n^2+28549128749256482272534517297024*n+129060101557903801655155119499920)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+17)-1/1536*(5051085842012942130708344447*n^4+384736565025205268053474412448*n^3+10997530534058925618564113146861*n^2+139815992257968946511708707625052*n+667039952062777219122553503645420)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+18)+1/1536*(18145364715482262435296643901*n^4+1455505979224421070501951977408*n^3+43810995353101779401993538063335*n^2+586477137597191142602537434591624*n+2945930762900589930864504722129772)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+19)-1/512*(19073163246089045457505447835*n^4+1608009850211436128793641544668*n^3+50868739292604990669238579190083*n^2+715628613054641261361870861582122*n+3777494689705630505405758672225892)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+20)-1/768*(2536573638916258405*n^4+85957187843108333564*n^3+1089549642800537231759*n^2+6119413427027976284836*n+12842249964648870648936)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+8)+1/768*(42961475477616931681*n^4+1579751887071302575347*n^3+21708815430061853651672*n^2+132063831871488179181516*n+299901212487664699335204)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+9)-1/768*(429313581062378521879*n^4+17325725431091481623108*n^3+261920598170244513064700*n^2+1758141435986343392898949*n+4422123743571418524938784)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+10)+1/768*(3931832256741707354551*n^4+177716889485307428421708*n^3+3021890282173536063177962*n^2+22922211342481308034900815*n+65478107519915821178554764)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+11)-1/1536*(76272860206548031541173*n^4+3844864924009331989185946*n^3+72967973020603793294476643*n^2+617998087682980338949652210*n+1971113073523156229727300468)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+12)+1/256*(119799252806196705045758*n^4+6617134170988312659251656*n^3+137468704129416950899678541*n^2+1273036521223900772166660613*n+4433830435464954066893467042)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+13)-1/768*(2993753853403555478783536*n^4+178795439951801145968923292*n^3+4012572965576814262975565705*n^2+40103530404171344435625603937*n+150599267919843110847999961158)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+14)-5/128*(147639598*n^4+1823656801*n^3+8489034741*n^2+17611864790*n+13701015230)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+2)-25/384*(2017458344*n^4+27000786667*n^3+137132414488*n^2+312830921003*n+269763700056)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+3)-5/384*(294368632728*n^4+3473927124319*n^3+9872532444945*n^2-14981839877500*n-71468866590666)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+4)-1/384*(10113241866724*n^4+338198236831735*n^3+3702094015023950*n^2+16859686099859675*n+27761444232335946)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+5)+1/384*(183194001991640*n^4-73737878880446*n^3-51166578570920369*n^2-453969721632817321*n-1136165615024160894)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+6)+1/768*(22191135638068315*n^4+709322089263594798*n^3+8428025943886686461*n^2+44099759260066003206*n+85695309961552010220)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+7)-5/64*(2*n+3)*(n+2)*(702184*n^2+4018079*n+5773516)/(n+70)/(n+69)/(n+67)/(n+71)*a(n+1), n >= 69
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 115
a(6) = 614
a(7) = 3504
a(8) = 20885
a(9) = 128292
a(10) = 805653
a(11) = 5145429
a(12) = 33303599
a(13) = 217908781
a(14) = 1438724862
a(15) = 9571907890
a(16) = 64101679227
a(17) = 431736779901
a(18) = 2922449260601
a(19) = 19870384374339
a(20) = 135641064945713
a(21) = 929240910500579
a(22) = 6386603302226684
a(23) = 44023956710482330
a(24) = 304281593265160497
a(25) = 2108306372658500908
a(26) = 14641271983684948936
a(27) = 101891127272240583862
a(28) = 710460827935633351673
a(29) = 4962847842292055280159
a(30) = 34726081323945323257852
a(31) = 243369870581272537634828
a(32) = 1708129797304985717387885
a(33) = 12005459038609995833694929
a(34) = 84489911897605221699486500
a(35) = 595342075793252768288493694
a(36) = 4199853386788803485520836431
a(37) = 29660615540345068794061072896
a(38) = 209690856811649720554969284270
a(39) = 1483914625019128791358683978884
a(40) = 10511070724524819258146599088440
a(41) = 74520153422794373693400942243514
a(42) = 528774868262578531523892021124834
a(43) = 3755095545889000304616460444568088
a(44) = 26687525673866155672433935803770268
a(45) = 189809454428188501933013280325376147
a(46) = 1350938686994473589798643322731872894
a(47) = 9621629950820172901656730176426908846
a(48) = 68571655760634842582733173114079328694
a(49) = 489003659657078160600474562096267970101
a(50) = 3489315739574008146588344423833012551087
a(51) = 24912594062930806323511796803719859487893
a(52) = 177966629698290257265458493872775542455187
a(53) = 1272008766810252555790503039331313768437318
a(54) = 9096304711031514816770277318433069566641166
a(55) = 65081145716526913705034507648326183604752304
a(56) = 465857436368946284747851516994186600083314050
a(57) = 3336193926038315050454263318322033727309519351
a(58) = 23902486822246007998320346662763857478462487188
a(59) = 171325462747608776816169032121733326882121288682
a(60) = 1228518133256716043582894542727952249646937578065
a(61) = 8812845763567082133218384746467549572478332938255
a(62) = 63244112334153007931068303247942859445189892382720
a(63) = 454033634052676934103664973001217568453670200728740
a(64) = 3260730089321017783053273761179414710940612995467863
a(65) = 23425869479590318337431680140034863394589310832297765
a(66) = 168354989638325608101167693314130120875303263506253804
a(67) = 1210322868730434220667177372118082671360315727245246340
a(68) = 8703966748602328373022471175384596308805668938690241220
a{\left(n + 69 \right)} = - \frac{2145 \left(n + 1\right) \left(n + 2\right) \left(2 n + 1\right) \left(2 n + 3\right) a{\left(n \right)}}{16 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{5 \left(n + 2\right) \left(2 n + 3\right) \left(702184 n^{2} + 4018079 n + 5773516\right) a{\left(n + 1 \right)}}{64 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(235 n^{2} + 31516 n + 1056496\right) a{\left(n + 68 \right)}}{2 \left(n + 67\right) \left(n + 71\right)} - \frac{\left(153413 n^{3} + 30726732 n^{2} + 2051154163 n + 45636029460\right) a{\left(n + 67 \right)}}{24 \left(n + 67\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(40402187 n^{4} + 10729982198 n^{3} + 1068504707581 n^{2} + 47285000606938 n + 784609684430016\right) a{\left(n + 66 \right)}}{192 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{5 \left(147639598 n^{4} + 1823656801 n^{3} + 8489034741 n^{2} + 17611864790 n + 13701015230\right) a{\left(n + 2 \right)}}{128 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(1737288148 n^{4} + 455387357667 n^{3} + 44759140396994 n^{2} + 1955061269811405 n + 32020688007132954\right) a{\left(n + 65 \right)}}{384 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{25 \left(2017458344 n^{4} + 27000786667 n^{3} + 137132414488 n^{2} + 312830921003 n + 269763700056\right) a{\left(n + 3 \right)}}{384 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(23235886495 n^{4} + 6029880561167 n^{3} + 586745940934688 n^{2} + 25372841278736920 n + 411413935531691376\right) a{\left(n + 64 \right)}}{384 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(206863224248 n^{4} + 54992295822609 n^{3} + 5472098351940862 n^{2} + 241590799540141443 n + 3993407830929459126\right) a{\left(n + 63 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{5 \left(294368632728 n^{4} + 3473927124319 n^{3} + 9872532444945 n^{2} - 14981839877500 n - 71468866590666\right) a{\left(n + 4 \right)}}{384 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(7009233775961 n^{4} + 1696784831262837 n^{3} + 153827794085358334 n^{2} + 6189362013836940990 n + 93247058079870094764\right) a{\left(n + 62 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(10113241866724 n^{4} + 338198236831735 n^{3} + 3702094015023950 n^{2} + 16859686099859675 n + 27761444232335946\right) a{\left(n + 5 \right)}}{384 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(183194001991640 n^{4} - 73737878880446 n^{3} - 51166578570920369 n^{2} - 453969721632817321 n - 1136165615024160894\right) a{\left(n + 6 \right)}}{384 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(218281568683475 n^{4} + 52743736012696770 n^{3} + 4776805995524500777 n^{2} + 192176032859293427112 n + 2897778994758860030982\right) a{\left(n + 61 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(7402619901340187 n^{4} + 1765011447347501652 n^{3} + 157752115783553661817 n^{2} + 6264022113223606067256 n + 93238287258855218336772\right) a{\left(n + 60 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(22191135638068315 n^{4} + 709322089263594798 n^{3} + 8428025943886686461 n^{2} + 44099759260066003206 n + 85695309961552010220\right) a{\left(n + 7 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(91086851275342523 n^{4} + 21372526156688262478 n^{3} + 1879880240350856484919 n^{2} + 73462209636814753699148 n + 1076143713700403798333856\right) a{\left(n + 59 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(436021605335092969 n^{4} + 100508951608476694437 n^{3} + 8684777917886067646475 n^{2} + 333391482428163369449313 n + 4797381987945343479598080\right) a{\left(n + 58 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(2536573638916258405 n^{4} + 85957187843108333564 n^{3} + 1089549642800537231759 n^{2} + 6119413427027976284836 n + 12842249964648870648936\right) a{\left(n + 8 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(3297773237259923850 n^{4} + 745303932617683742653 n^{3} + 63131736449977288562571 n^{2} + 2375445868049650632661790 n + 33499199250123676293923892\right) a{\left(n + 57 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(42961475477616931681 n^{4} + 1579751887071302575347 n^{3} + 21708815430061853651672 n^{2} + 132063831871488179181516 n + 299901212487664699335204\right) a{\left(n + 9 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(76808308241162490495 n^{4} + 16953174586251190235578 n^{3} + 1401952096572971109836325 n^{2} + 51478198556222870645091650 n + 708135552306043077943090968\right) a{\left(n + 56 \right)}}{3072 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(91749947722823911371 n^{4} + 14190648596863478647338 n^{3} + 675441576831345042441381 n^{2} + 6582776975828857032150702 n - 159758798404967841515864744\right) a{\left(n + 54 \right)}}{1024 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(152218632569691298115 n^{4} + 32394201545327128853832 n^{3} + 2578532550279009457177921 n^{2} + 90961165397446036583550264 n + 1199493508504786268652583884\right) a{\left(n + 55 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(429313581062378521879 n^{4} + 17325725431091481623108 n^{3} + 261920598170244513064700 n^{2} + 1758141435986343392898949 n + 4422123743571418524938784\right) a{\left(n + 10 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(1971059264981038690359 n^{4} + 446426083033959255727855 n^{3} + 37853327346224445331390767 n^{2} + 1424306180392529027160116003 n + 20068240053619060452317279760\right) a{\left(n + 53 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(3931832256741707354551 n^{4} + 177716889485307428421708 n^{3} + 3021890282173536063177962 n^{2} + 22922211342481308034900815 n + 65478107519915821178554764\right) a{\left(n + 11 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(42385912053065919534199 n^{4} + 9152326979000713434379432 n^{3} + 741223302992689579938137855 n^{2} + 26684362138407435502633824842 n + 360300637249061738797934958096\right) a{\left(n + 52 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(76272860206548031541173 n^{4} + 3844864924009331989185946 n^{3} + 72967973020603793294476643 n^{2} + 617998087682980338949652210 n + 1971113073523156229727300468\right) a{\left(n + 12 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(119799252806196705045758 n^{4} + 6617134170988312659251656 n^{3} + 137468704129416950899678541 n^{2} + 1273036521223900772166660613 n + 4433830435464954066893467042\right) a{\left(n + 13 \right)}}{256 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(138668549985878719425449 n^{4} + 29138976566398334202079068 n^{3} + 2297344444000507054456800457 n^{2} + 80541087316298781178831950288 n + 1059398952063320394836714213274\right) a{\left(n + 51 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(1346244465440653430663463 n^{4} + 276519885050316744899319914 n^{3} + 21315720693393827204346233127 n^{2} + 730855043580593155233567508228 n + 9404439156471865731631516936680\right) a{\left(n + 50 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(1865706855020779402988606 n^{4} + 337619766548255929754887401 n^{3} + 21916814847860438564820349849 n^{2} + 595062656304366902736826663278 n + 5500972362511773333660589940712\right) a{\left(n + 47 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(2445116652422354506802171 n^{4} + 491790316042958704462705982 n^{3} + 37138827745920936521504976115 n^{2} + 1248049798566496653796558550536 n + 15747221141753126004219370652640\right) a{\left(n + 49 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(2993753853403555478783536 n^{4} + 178795439951801145968923292 n^{3} + 4012572965576814262975565705 n^{2} + 40103530404171344435625603937 n + 150599267919843110847999961158\right) a{\left(n + 14 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(21068231881131528479674309 n^{4} + 1348135379299291062799367623 n^{3} + 32396802315192558565719149297 n^{2} + 346498340861416037242538295743 n + 1391622802111359221531063027316\right) a{\left(n + 15 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(22658408003102384695413369 n^{4} + 4471916314078392263455920242 n^{3} + 331832380923228756606123476655 n^{2} + 10971972617920553668403354537326 n + 136392186774435429109246503322296\right) a{\left(n + 48 \right)}}{3072 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(123569104538644310114470026 n^{4} + 8416101533075995817586444593 n^{3} + 215185680204527765972857584561 n^{2} + 2447869308255199158750396871750 n + 10452784915940647484121485217510\right) a{\left(n + 16 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(426368762686738385856868043 n^{4} + 79962053782487559764511955834 n^{3} + 5610078521066060508405563446909 n^{2} + 174497166493236758823508010615318 n + 2030063323590418217385920210630784\right) a{\left(n + 46 \right)}}{3072 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(709763180751513107925949002 n^{4} + 130521848228277050490392575061 n^{3} + 8989616094463547913404417028567 n^{2} + 274826730727480146733939644890104 n + 3146545883550275627256575964126210\right) a{\left(n + 45 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(1213142275404096173535906245 n^{4} + 87526676820894000217643499232 n^{3} + 2370150458974274731882004258791 n^{2} + 28549128749256482272534517297024 n + 129060101557903801655155119499920\right) a{\left(n + 17 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(1641786441114063188318987711 n^{4} + 295582175485002365766743047010 n^{3} + 19938935012288379294329714712583 n^{2} + 597263189039959938322631050369336 n + 6703079484537241412642815439511297\right) a{\left(n + 44 \right)}}{384 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(5051085842012942130708344447 n^{4} + 384736565025205268053474412448 n^{3} + 10997530534058925618564113146861 n^{2} + 139815992257968946511708707625052 n + 667039952062777219122553503645420\right) a{\left(n + 18 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(12344385918221301341630451622 n^{4} + 2174294477931303696994658342770 n^{3} + 143521873227747080531774449661567 n^{2} + 4207745421425345651510894963773097 n + 46229632279516446561208378869002496\right) a{\left(n + 43 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(18145364715482262435296643901 n^{4} + 1455505979224421070501951977408 n^{3} + 43810995353101779401993538063335 n^{2} + 586477137597191142602537434591624 n + 2945930762900589930864504722129772\right) a{\left(n + 19 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(19073163246089045457505447835 n^{4} + 1608009850211436128793641544668 n^{3} + 50868739292604990669238579190083 n^{2} + 715628613054641261361870861582122 n + 3777494689705630505405758672225892\right) a{\left(n + 20 \right)}}{512 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(79477940597878402843018610261 n^{4} + 13688083847262389209385568137072 n^{3} + 883575481330240066707419889413683 n^{2} + 25335648111729962276944260767226700 n + 272281138248748951425933934291723788\right) a{\left(n + 42 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(160793411296706179038204237099 n^{4} + 14222881860468674413064202365404 n^{3} + 472037463901508561915331401618463 n^{2} + 6966469444609884182605407340743242 n + 38574590799811433598159726020865840\right) a{\left(n + 21 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(224501774614696983138176899735 n^{4} + 37786307042831947076495909823758 n^{3} + 2383914578623164744910525310686649 n^{2} + 66814696458247534467322801837611226 n + 701922836420470335439027649407873788\right) a{\left(n + 41 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(468109857861216042447835020884 n^{4} + 45329510977577195286365832659110 n^{3} + 1646677346298972645268303017243583 n^{2} + 26595505822747774547527751925679217 n + 161133460941834019776338107882405332\right) a{\left(n + 23 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(563988132692675320070057095021 n^{4} + 92719561424331622999309619891786 n^{3} + 5714009004689790820575385885593593 n^{2} + 156445435131672996163407636366974728 n + 1605643459925282062618422373485556260\right) a{\left(n + 40 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(814511191584175713394865290077 n^{4} + 75455669155327180869380726928698 n^{3} + 2622539999086509128251392003222915 n^{2} + 40528964752403857208176807546483918 n + 234977891025247448115079045935867384\right) a{\left(n + 22 \right)}}{3072 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(1270438242868496944349248752703 n^{4} + 203892293485622584685653035762990 n^{3} + 12266946968476764965229707421598049 n^{2} + 327903039326548960384502571888116274 n + 3285792298916521849226818965938737824\right) a{\left(n + 39 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(1289800930694240884846804344209 n^{4} + 201958915933780294727320648725862 n^{3} + 11855172231669781206149856250112878 n^{2} + 309202142536102159985538711983095715 n + 3023290014942033819053172823256178006\right) a{\left(n + 38 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(3402640943970975497549036173923 n^{4} + 385555204028835431861658800199518 n^{3} + 16383140264649935630477470661481341 n^{2} + 309407530310646320020222714463550082 n + 2191282993015071755525484737032145600\right) a{\left(n + 27 \right)}}{512 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(3734994513176976837276237801845 n^{4} + 392766533725825581537902205251356 n^{3} + 15491248508710996034368868980739449 n^{2} + 271597683532428578663848817645788502 n + 1785917182541769787235328760548711108\right) a{\left(n + 25 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(3918906120140980926086415671449 n^{4} + 395867848982142605097208346494762 n^{3} + 14999801843459566246108344690733607 n^{2} + 252667670344546497011605589433329222 n + 1596427556260048464432248411694546264\right) a{\left(n + 24 \right)}}{3072 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(3944012103520209303656419233028 n^{4} + 586744535212034533499156852189471 n^{3} + 32725672925805441044881377108522074 n^{2} + 811040856803020551139033046141304307 n + 7535724535547288834342448419118101592\right) a{\left(n + 36 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(3974169156407476918709795945657 n^{4} + 575706214060082561397617074337284 n^{3} + 31267549962569425856578974152283531 n^{2} + 754590322553815116288148977901799172 n + 6827579385663410890567351931477081656\right) a{\left(n + 35 \right)}}{512 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(4737677638289416679609595343639 n^{4} + 723323033488004628459167356203148 n^{3} + 41401561407640373198093120710987865 n^{2} + 1052941935996603425438145037552967936 n + 10039420770762418702116379209933698484\right) a{\left(n + 37 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(6477528922882912454602034951163 n^{4} + 707716099098347993196622776029840 n^{3} + 28998741186452751910194301457314317 n^{2} + 528142681527488848118232697442650156 n + 3607321251397618916991065859636119880\right) a{\left(n + 26 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(7301676348292086109783244707997 n^{4} + 856663703648890593982996219573718 n^{3} + 37689007439533836438217876937570386 n^{2} + 736918881709161972639641978036471845 n + 5403026605242558270299664650739738612\right) a{\left(n + 28 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(8185913756073408436673452250954 n^{4} + 1153837941022339269851644855809626 n^{3} + 60977495104996851836106247879804627 n^{2} + 1431949282834147287842232675094288099 n + 12607610838737263039674935774691407598\right) a{\left(n + 34 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(9478096638003299160009932781277 n^{4} + 1149746230092757574052210483332420 n^{3} + 52297548122479333106091332009680949 n^{2} + 1057168133622924071463386008859046136 n + 8013141247760999226696287731400912514\right) a{\left(n + 29 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(11933911136070629195402527182599 n^{4} + 1541867740313376804304781300837652 n^{3} + 74693850064294164013869533490733426 n^{2} + 1607984502759780705544117957140858435 n + 12979312748452685168830805540310434580\right) a{\left(n + 31 \right)}}{768 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} + \frac{\left(20430733537045546383566237554539 n^{4} + 2799886232139713160089368306775546 n^{3} + 143864049856553224602272122787696145 n^{2} + 3284776634229296888020743180445967326 n + 28119972833901870703643271321371373804\right) a{\left(n + 33 \right)}}{1536 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(44653728311574386136752137167319 n^{4} + 5593422808232503654088888712253922 n^{3} + 262713323334424520517769797594827201 n^{2} + 5483484044883268392775177044148525798 n + 42915509512304167190972929140634305144\right) a{\left(n + 30 \right)}}{3072 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)} - \frac{\left(46337294869700488078397754611923 n^{4} + 6168701371664858309379022915371518 n^{3} + 307907892955331938382140576742105933 n^{2} + 6829643069319863263530011844207377914 n + 56798785261461265829554496987613230856\right) a{\left(n + 32 \right)}}{3072 \left(n + 67\right) \left(n + 69\right) \left(n + 70\right) \left(n + 71\right)}, \quad n \geq 69
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24819/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[19,x]*F[7,x]
F[7,x] = F[43,x]+F[8,x]
F[8,x] = F[23,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[19,x]
F[12,x] = F[13,x]+F[20,x]
F[13,x] = F[14,x]+F[9,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]+F[2,x]
F[16,x] = -F[2,x]+F[5,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[19,x]*F[2,x]
F[19,x] = x
F[20,x] = -F[14,x]+F[21,x]
F[21,x] = 1/F[19,x]*F[22,x]
F[22,x] = F[16,x]
F[23,x] = F[24,x]
F[24,x] = F[19,x]*F[25,x]
F[25,x] = F[26,x]+F[40,x]
F[26,x] = F[27,x]+F[8,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[19,x]*F[29,x]
F[29,x] = F[0,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[0,x]*F[19,x]*F[32,x]
F[32,x] = F[29,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[19,x]*F[35,x]
F[35,x] = 1/F[19,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[19,x]*F[32,x]*F[38,x]
F[38,x] = 1/F[0,x]/F[19,x]*F[39,x]
F[39,x] = F[30,x]
F[40,x] = F[20,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[19,x]*F[20,x]*F[32,x]
F[43,x] = F[44,x]+F[74,x]
F[44,x] = F[45,x]
F[45,x] = F[19,x]*F[46,x]
F[46,x] = F[47,x]+F[63,x]
F[47,x] = F[48,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[0,x]^2*F[50,x]
F[50,x] = 1/F[19,x]*F[51,x]
F[51,x] = F[2,x]
F[52,x] = F[53,x]+F[61,x]
F[53,x] = F[54,x]+F[59,x]
F[54,x] = F[10,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[19,x]*F[57,x]
F[57,x] = F[54,x]+F[58,x]
F[58,x] = F[30,x]*F[5,x]
F[59,x] = F[60,x]
F[60,x] = F[19,x]*F[52,x]
F[61,x] = F[0,x]*F[30,x]*F[62,x]
F[62,x] = -F[0,x]+F[50,x]
F[63,x] = F[64,x]
F[64,x] = -F[83,x]+F[65,x]
F[65,x] = 1/F[19,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = -F[78,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[19,x]*F[70,x]
F[70,x] = 1/F[19,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = -F[4,x]+F[8,x]
F[74,x] = F[75,x]
F[75,x] = F[19,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[19,x]*F[32,x]*F[46,x]
F[78,x] = F[2,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[19,x]*F[81,x]
F[81,x] = F[57,x]+F[82,x]
F[82,x] = F[2,x]*F[4,x]
F[83,x] = F[84,x]
F[84,x] = F[85,x]+F[88,x]
F[85,x] = F[23,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[19,x]*F[84,x]
F[88,x] = F[89,x]
F[89,x] = F[2,x]*F[29,x]*F[62,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{19}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{43}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{23}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{20}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right) F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = -F_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{16}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{40}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{8}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{0}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{19}\! \left(x \right) F_{32}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{0}\! \left(x \right) F_{19}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{30}\! \left(x \right)
F_{40}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{19}\! \left(x \right) F_{20}\! \left(x \right) F_{32}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{74}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{19}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{63}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{2}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{61}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{59}\! \left(x \right)
F_{54}\! \left(x \right) = F_{10}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{54}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{30}\! \left(x \right) F_{5}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{19}\! \left(x \right) F_{52}\! \left(x \right)
F_{61}\! \left(x \right) = F_{0}\! \left(x \right) F_{30}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{50}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{19}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{8}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{19}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{19}\! \left(x \right) F_{32}\! \left(x \right) F_{46}\! \left(x \right)
F_{78}\! \left(x \right) = F_{2}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{19}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{57}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{88}\! \left(x \right)
F_{85}\! \left(x \right) = F_{23}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{19}\! \left(x \right) F_{84}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{2}\! \left(x \right) F_{29}\! \left(x \right) F_{62}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_19(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_19(x)*F_7(x))
Eq(F_7(x), F_43(x) + F_8(x))
Eq(F_8(x), F_23(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_19(x))
Eq(F_12(x), F_13(x) + F_20(x))
Eq(F_13(x), F_14(x) + F_9(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x) + F_2(x))
Eq(F_16(x), -F_2(x) + F_5(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_19(x)*F_2(x))
Eq(F_19(x), x)
Eq(F_20(x), -F_14(x) + F_21(x))
Eq(F_21(x), F_22(x)/F_19(x))
Eq(F_22(x), F_16(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_19(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_40(x))
Eq(F_26(x), F_27(x) + F_8(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_19(x)*F_29(x))
Eq(F_29(x), F_0(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_0(x)*F_19(x)*F_32(x))
Eq(F_32(x), F_29(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_19(x)*F_35(x))
Eq(F_35(x), F_36(x)/F_19(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_19(x)*F_32(x)*F_38(x))
Eq(F_38(x), F_39(x)/(F_0(x)*F_19(x)))
Eq(F_39(x), F_30(x))
Eq(F_40(x), F_20(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_19(x)*F_20(x)*F_32(x))
Eq(F_43(x), F_44(x) + F_74(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_19(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_63(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_0(x)**2*F_50(x))
Eq(F_50(x), F_51(x)/F_19(x))
Eq(F_51(x), F_2(x))
Eq(F_52(x), F_53(x) + F_61(x))
Eq(F_53(x), F_54(x) + F_59(x))
Eq(F_54(x), F_10(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_19(x)*F_57(x))
Eq(F_57(x), F_54(x) + F_58(x))
Eq(F_58(x), F_30(x)*F_5(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_19(x)*F_52(x))
Eq(F_61(x), F_0(x)*F_30(x)*F_62(x))
Eq(F_62(x), -F_0(x) + F_50(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_65(x) - F_83(x))
Eq(F_65(x), F_66(x)/F_19(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_68(x) - F_78(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_19(x)*F_70(x))
Eq(F_70(x), F_71(x)/F_19(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), -F_4(x) + F_8(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_19(x)*F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_19(x)*F_32(x)*F_46(x))
Eq(F_78(x), F_2(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_19(x)*F_81(x))
Eq(F_81(x), F_57(x) + F_82(x))
Eq(F_82(x), F_2(x)*F_4(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_85(x) + F_88(x))
Eq(F_85(x), F_23(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_19(x)*F_84(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_2(x)*F_29(x)*F_62(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 0]]}]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], 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[2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: point_and_col_placements_req_corrob
Tree: http://www.permpal.com/tree/24856/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[186,x]+F[7,x]+F[8,x]
F[7,x] = 0
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[6,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[4,x]
F[12,x] = F[13,x]+F[164,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[4,x]
F[15,x] = 1/F[4,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = -F[107,x]+F[18,x]
F[18,x] = F[19,x]+F[5,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[161,x]+F[22,x]
F[22,x] = F[18,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[27,x]*F[4,x]
F[25,x] = 1/F[4,x]*F[26,x]
F[26,x] = F[6,x]
F[27,x] = F[0,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[0,x]*F[30,x]*F[4,x]
F[30,x] = -F[148,x]+F[31,x]
F[31,x] = F[138,x]+F[32,x]
F[32,x] = F[27,x]+F[33,x]
F[33,x] = F[34,x]+F[6,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[30,x]*F[6,x]
F[38,x] = F[39,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[133,x]+F[137,x]+F[41,x]+F[78,x]
F[41,x] = 1/F[4,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[30,x]+F[44,x]
F[44,x] = F[45,x]+F[51,x]
F[45,x] = F[27,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[25,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[25,x]*F[30,x]*F[4,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[70,x]
F[54,x] = F[5,x]*F[55,x]
F[55,x] = 1/F[4,x]*F[56,x]
F[56,x] = -F[1,x]-F[57,x]-F[58,x]+F[30,x]
F[57,x] = F[4,x]*F[44,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[30,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[30,x]*F[4,x]*F[62,x]
F[62,x] = 1/F[4,x]*F[63,x]
F[63,x] = -F[1,x]-F[64,x]+F[27,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[68,x]
F[66,x] = 1/F[4,x]*F[67,x]
F[67,x] = F[2,x]
F[68,x] = F[69,x]
F[69,x] = F[4,x]*F[62,x]*F[66,x]
F[70,x] = F[71,x]
F[71,x] = F[0,x]*F[4,x]*F[5,x]*F[72,x]
F[72,x] = 1/F[4,x]*F[73,x]
F[73,x] = -F[1,x]-F[56,x]-F[58,x]-F[74,x]+F[59,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[44,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[4,x]*F[5,x]*F[72,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[40,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[30,x]*F[82,x]
F[82,x] = 1/F[0,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = -F[93,x]+F[85,x]
F[85,x] = 1/F[4,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = -F[124,x]+F[88,x]
F[88,x] = 1/F[4,x]*F[89,x]
F[89,x] = -F[0,x]-F[117,x]-F[129,x]-F[132,x]+F[90,x]
F[90,x] = F[25,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = 1/F[4,x]*F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[101,x]+F[96,x]
F[96,x] = F[6,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[96,x]
F[100,x] = F[28,x]*F[6,x]
F[101,x] = F[102,x]
F[102,x] = -F[17,x]+F[103,x]
F[103,x] = -F[109,x]+F[104,x]
F[104,x] = 1/F[4,x]*F[105,x]
F[105,x] = F[106,x]
F[106,x] = -F[0,x]+F[107,x]
F[107,x] = 1/F[4,x]*F[108,x]
F[108,x] = F[2,x]
F[109,x] = F[110,x]+F[5,x]
F[110,x] = F[111,x]+F[115,x]
F[111,x] = F[112,x]+F[2,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[103,x]+F[110,x]
F[115,x] = F[116,x]
F[116,x] = F[2,x]*F[25,x]*F[4,x]
F[117,x] = F[118,x]
F[118,x] = F[0,x]*F[119,x]*F[4,x]
F[119,x] = F[120,x]+F[127,x]
F[120,x] = 1/F[0,x]/F[4,x]*F[121,x]
F[121,x] = F[122,x]
F[122,x] = -F[0,x]-F[123,x]-F[126,x]+F[25,x]
F[123,x] = F[124,x]*F[4,x]
F[124,x] = 1/F[4,x]*F[125,x]
F[125,x] = F[9,x]
F[126,x] = F[4,x]*F[90,x]
F[127,x] = F[128,x]
F[128,x] = -F[32,x]+F[120,x]
F[129,x] = F[130,x]*F[4,x]
F[130,x] = F[131,x]+F[90,x]
F[131,x] = F[91,x]
F[132,x] = F[25,x]*F[4,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[30,x]*F[4,x]
F[135,x] = 1/F[4,x]*F[136,x]
F[136,x] = F[128,x]
F[137,x] = F[4,x]*F[40,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]*F[4,x]
F[140,x] = F[141,x]+F[146,x]
F[141,x] = F[142,x]+F[143,x]
F[142,x] = F[120,x]*F[27,x]
F[143,x] = F[144,x]+F[95,x]
F[144,x] = F[145,x]
F[145,x] = F[30,x]*F[4,x]*F[95,x]
F[146,x] = F[147,x]
F[147,x] = F[135,x]*F[30,x]*F[4,x]
F[148,x] = F[149,x]+F[33,x]
F[149,x] = F[150,x]
F[150,x] = F[151,x]*F[4,x]
F[151,x] = F[152,x]+F[155,x]
F[152,x] = F[143,x]+F[153,x]
F[153,x] = F[154,x]*F[27,x]
F[154,x] = -F[62,x]+F[120,x]
F[155,x] = -F[156,x]+F[146,x]
F[156,x] = F[157,x]
F[157,x] = F[158,x]*F[30,x]*F[4,x]
F[158,x] = 1/F[4,x]*F[159,x]
F[159,x] = F[160,x]
F[160,x] = -F[27,x]+F[62,x]
F[161,x] = F[103,x]+F[162,x]
F[162,x] = F[163,x]
F[163,x] = F[103,x]*F[30,x]*F[4,x]
F[164,x] = F[165,x]
F[165,x] = F[166,x]*F[4,x]
F[166,x] = F[167,x]+F[184,x]
F[167,x] = F[168,x]+F[182,x]
F[168,x] = 1/F[4,x]*F[169,x]
F[169,x] = F[170,x]
F[170,x] = -F[173,x]+F[171,x]
F[171,x] = 1/F[4,x]*F[172,x]
F[172,x] = F[34,x]
F[173,x] = F[174,x]
F[174,x] = F[175,x]*F[4,x]
F[175,x] = F[176,x]+F[178,x]
F[176,x] = 1/F[4,x]*F[177,x]
F[177,x] = F[42,x]
F[178,x] = F[179,x]*F[4,x]
F[179,x] = F[175,x]+F[180,x]
F[180,x] = F[181,x]
F[181,x] = F[0,x]*F[6,x]*F[72,x]
F[182,x] = F[183,x]
F[183,x] = F[15,x]*F[4,x]*F[55,x]
F[184,x] = F[185,x]
F[185,x] = F[15,x]*F[4,x]*F[59,x]
F[186,x] = F[32,x]*F[4,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{186}\! \left(x \right)+F_{7}\! \left(x \right)+F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = 0
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{164}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{107}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{5}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{161}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{6}\! \left(x \right)
F_{27}\! \left(x \right) = F_{0}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{0}\! \left(x \right) F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{148}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{138}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{27}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{6}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{30}\! \left(x \right) F_{6}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{133}\! \left(x \right)+F_{137}\! \left(x \right)+F_{41}\! \left(x \right)+F_{78}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{51}\! \left(x \right)
F_{45}\! \left(x \right) = F_{27}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{25}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{25}\! \left(x \right) F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{70}\! \left(x \right)
F_{54}\! \left(x \right) = F_{5}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{56}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{57}\! \left(x \right)-F_{58}\! \left(x \right)+F_{30}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{30}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{63}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{64}\! \left(x \right)+F_{27}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{68}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{2}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right) F_{66}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{5}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = \frac{F_{73}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{73}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{56}\! \left(x \right)-F_{58}\! \left(x \right)-F_{74}\! \left(x \right)+F_{59}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{44}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right) F_{72}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{40}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{30}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{93}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{124}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{89}\! \left(x \right) = -F_{0}\! \left(x \right)-F_{117}\! \left(x \right)-F_{129}\! \left(x \right)-F_{132}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{25}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{101}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{6}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{96}\! \left(x \right)
F_{100}\! \left(x \right) = F_{28}\! \left(x \right) F_{6}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = -F_{17}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{109}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = \frac{F_{108}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{108}\! \left(x \right) = F_{2}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{5}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{115}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{2}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{103}\! \left(x \right)+F_{110}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{2}\! \left(x \right) F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{0}\! \left(x \right) F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{127}\! \left(x \right)
F_{120}\! \left(x \right) = \frac{F_{121}\! \left(x \right)}{F_{0}\! \left(x \right) F_{4}\! \left(x \right)}
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = -F_{0}\! \left(x \right)-F_{123}\! \left(x \right)-F_{126}\! \left(x \right)+F_{25}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{4}\! \left(x \right)
F_{124}\! \left(x \right) = \frac{F_{125}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{125}\! \left(x \right) = F_{9}\! \left(x \right)
F_{126}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{120}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{90}\! \left(x \right)
F_{131}\! \left(x \right) = F_{91}\! \left(x \right)
F_{132}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{135}\! \left(x \right) = \frac{F_{136}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{136}\! \left(x \right) = F_{128}\! \left(x \right)
F_{137}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{146}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{143}\! \left(x \right)
F_{142}\! \left(x \right) = F_{120}\! \left(x \right) F_{27}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{95}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{135}\! \left(x \right) F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{33}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right) F_{4}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{155}\! \left(x \right)
F_{152}\! \left(x \right) = F_{143}\! \left(x \right)+F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{27}\! \left(x \right)
F_{154}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{120}\! \left(x \right)
F_{155}\! \left(x \right) = -F_{156}\! \left(x \right)+F_{146}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{158}\! \left(x \right) = \frac{F_{159}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = -F_{27}\! \left(x \right)+F_{62}\! \left(x \right)
F_{161}\! \left(x \right) = F_{103}\! \left(x \right)+F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{103}\! \left(x \right) F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{4}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{184}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{182}\! \left(x \right)
F_{168}\! \left(x \right) = \frac{F_{169}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = -F_{173}\! \left(x \right)+F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = \frac{F_{172}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{172}\! \left(x \right) = F_{34}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right) F_{4}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)+F_{178}\! \left(x \right)
F_{176}\! \left(x \right) = \frac{F_{177}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{177}\! \left(x \right) = F_{42}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right) F_{4}\! \left(x \right)
F_{179}\! \left(x \right) = F_{175}\! \left(x \right)+F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{0}\! \left(x \right) F_{6}\! \left(x \right) F_{72}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{186}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_186(x) + F_7(x) + F_8(x))
Eq(F_7(x), 0)
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_6(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_4(x))
Eq(F_12(x), F_13(x) + F_164(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x)/F_4(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), -F_107(x) + F_18(x))
Eq(F_18(x), F_19(x) + F_5(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_161(x) + F_22(x))
Eq(F_22(x), F_18(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_27(x)*F_4(x))
Eq(F_25(x), F_26(x)/F_4(x))
Eq(F_26(x), F_6(x))
Eq(F_27(x), F_0(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_0(x)*F_30(x)*F_4(x))
Eq(F_30(x), -F_148(x) + F_31(x))
Eq(F_31(x), F_138(x) + F_32(x))
Eq(F_32(x), F_27(x) + F_33(x))
Eq(F_33(x), F_34(x) + F_6(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_30(x)*F_6(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_133(x) + F_137(x) + F_41(x) + F_78(x))
Eq(F_41(x), F_42(x)/F_4(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), -F_30(x) + F_44(x))
Eq(F_44(x), F_45(x) + F_51(x))
Eq(F_45(x), F_27(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_25(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_25(x)*F_30(x)*F_4(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_70(x))
Eq(F_54(x), F_5(x)*F_55(x))
Eq(F_55(x), F_56(x)/F_4(x))
Eq(F_56(x), -F_1(x) + F_30(x) - F_57(x) - F_58(x))
Eq(F_57(x), F_4(x)*F_44(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_30(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_30(x)*F_4(x)*F_62(x))
Eq(F_62(x), F_63(x)/F_4(x))
Eq(F_63(x), -F_1(x) + F_27(x) - F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_68(x))
Eq(F_66(x), F_67(x)/F_4(x))
Eq(F_67(x), F_2(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_4(x)*F_62(x)*F_66(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_0(x)*F_4(x)*F_5(x)*F_72(x))
Eq(F_72(x), F_73(x)/F_4(x))
Eq(F_73(x), -F_1(x) - F_56(x) - F_58(x) + F_59(x) - F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_44(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_4(x)*F_5(x)*F_72(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_40(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_30(x)*F_82(x))
Eq(F_82(x), F_83(x)/F_0(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_85(x) - F_93(x))
Eq(F_85(x), F_86(x)/F_4(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), -F_124(x) + F_88(x))
Eq(F_88(x), F_89(x)/F_4(x))
Eq(F_89(x), -F_0(x) - F_117(x) - F_129(x) - F_132(x) + F_90(x))
Eq(F_90(x), F_25(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_94(x)/F_4(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_101(x) + F_96(x))
Eq(F_96(x), F_6(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_96(x))
Eq(F_100(x), F_28(x)*F_6(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x) - F_17(x))
Eq(F_103(x), F_104(x) - F_109(x))
Eq(F_104(x), F_105(x)/F_4(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), -F_0(x) + F_107(x))
Eq(F_107(x), F_108(x)/F_4(x))
Eq(F_108(x), F_2(x))
Eq(F_109(x), F_110(x) + F_5(x))
Eq(F_110(x), F_111(x) + F_115(x))
Eq(F_111(x), F_112(x) + F_2(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_103(x) + F_110(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_2(x)*F_25(x)*F_4(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_0(x)*F_119(x)*F_4(x))
Eq(F_119(x), F_120(x) + F_127(x))
Eq(F_120(x), F_121(x)/(F_0(x)*F_4(x)))
Eq(F_121(x), F_122(x))
Eq(F_122(x), -F_0(x) - F_123(x) - F_126(x) + F_25(x))
Eq(F_123(x), F_124(x)*F_4(x))
Eq(F_124(x), F_125(x)/F_4(x))
Eq(F_125(x), F_9(x))
Eq(F_126(x), F_4(x)*F_90(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_120(x) - F_32(x))
Eq(F_129(x), F_130(x)*F_4(x))
Eq(F_130(x), F_131(x) + F_90(x))
Eq(F_131(x), F_91(x))
Eq(F_132(x), F_25(x)*F_4(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_30(x)*F_4(x))
Eq(F_135(x), F_136(x)/F_4(x))
Eq(F_136(x), F_128(x))
Eq(F_137(x), F_4(x)*F_40(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x)*F_4(x))
Eq(F_140(x), F_141(x) + F_146(x))
Eq(F_141(x), F_142(x) + F_143(x))
Eq(F_142(x), F_120(x)*F_27(x))
Eq(F_143(x), F_144(x) + F_95(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_30(x)*F_4(x)*F_95(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_135(x)*F_30(x)*F_4(x))
Eq(F_148(x), F_149(x) + F_33(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_151(x)*F_4(x))
Eq(F_151(x), F_152(x) + F_155(x))
Eq(F_152(x), F_143(x) + F_153(x))
Eq(F_153(x), F_154(x)*F_27(x))
Eq(F_154(x), F_120(x) - F_62(x))
Eq(F_155(x), F_146(x) - F_156(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_158(x)*F_30(x)*F_4(x))
Eq(F_158(x), F_159(x)/F_4(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), -F_27(x) + F_62(x))
Eq(F_161(x), F_103(x) + F_162(x))
Eq(F_162(x), F_163(x))
Eq(F_163(x), F_103(x)*F_30(x)*F_4(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_166(x)*F_4(x))
Eq(F_166(x), F_167(x) + F_184(x))
Eq(F_167(x), F_168(x) + F_182(x))
Eq(F_168(x), F_169(x)/F_4(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_171(x) - F_173(x))
Eq(F_171(x), F_172(x)/F_4(x))
Eq(F_172(x), F_34(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_175(x)*F_4(x))
Eq(F_175(x), F_176(x) + F_178(x))
Eq(F_176(x), F_177(x)/F_4(x))
Eq(F_177(x), F_42(x))
Eq(F_178(x), F_179(x)*F_4(x))
Eq(F_179(x), F_175(x) + F_180(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_0(x)*F_6(x)*F_72(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_15(x)*F_4(x)*F_55(x))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_15(x)*F_4(x)*F_59(x))
Eq(F_186(x), F_32(x)*F_4(x))
Pack JSON:
{"name": "point_and_col_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
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[3, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 1], [3, 1], [3, 2], [3, 1], [3, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 1], [3, 1], [3, 1], [3, 2], [3, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 2], [3, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 1], [3, 1], [3, 2], [3, 1], [3, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [0, 1], [3, 1], [3, 2], [3, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [2, 1], [3, 1], [3, 2], [3, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[2, 1], [2, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[2, 1], [2, 1], [3, 1], [3, 2], [3, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[2, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[2, 1], [3, 1], [3, 1], [3, 2], [3, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 2], [3, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 6]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 5]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25812/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[19,x]*F[7,x]
F[7,x] = F[43,x]+F[8,x]
F[8,x] = F[23,x]+F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[19,x]
F[12,x] = F[13,x]+F[20,x]
F[13,x] = F[14,x]+F[9,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]+F[2,x]
F[16,x] = -F[2,x]+F[5,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[19,x]*F[2,x]
F[19,x] = x
F[20,x] = -F[14,x]+F[21,x]
F[21,x] = 1/F[19,x]*F[22,x]
F[22,x] = F[16,x]
F[23,x] = F[24,x]
F[24,x] = F[19,x]*F[25,x]
F[25,x] = F[26,x]+F[40,x]
F[26,x] = F[27,x]+F[8,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[19,x]*F[29,x]
F[29,x] = F[0,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[0,x]*F[19,x]*F[32,x]
F[32,x] = F[29,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[19,x]*F[35,x]
F[35,x] = 1/F[19,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[19,x]*F[32,x]*F[38,x]
F[38,x] = 1/F[0,x]/F[19,x]*F[39,x]
F[39,x] = F[30,x]
F[40,x] = F[20,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[19,x]*F[20,x]*F[32,x]
F[43,x] = F[44,x]+F[74,x]
F[44,x] = F[45,x]
F[45,x] = F[19,x]*F[46,x]
F[46,x] = F[47,x]+F[63,x]
F[47,x] = F[48,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[0,x]^2*F[50,x]
F[50,x] = 1/F[19,x]*F[51,x]
F[51,x] = F[2,x]
F[52,x] = F[53,x]+F[61,x]
F[53,x] = F[54,x]+F[59,x]
F[54,x] = F[10,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[19,x]*F[57,x]
F[57,x] = F[54,x]+F[58,x]
F[58,x] = F[30,x]*F[5,x]
F[59,x] = F[60,x]
F[60,x] = F[19,x]*F[52,x]
F[61,x] = F[0,x]*F[30,x]*F[62,x]
F[62,x] = -F[0,x]+F[50,x]
F[63,x] = F[64,x]
F[64,x] = -F[83,x]+F[65,x]
F[65,x] = 1/F[19,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = -F[78,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[19,x]*F[70,x]
F[70,x] = 1/F[19,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = -F[4,x]+F[8,x]
F[74,x] = F[75,x]
F[75,x] = F[19,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[19,x]*F[32,x]*F[46,x]
F[78,x] = F[2,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[19,x]*F[81,x]
F[81,x] = F[57,x]+F[82,x]
F[82,x] = F[2,x]*F[4,x]
F[83,x] = F[84,x]
F[84,x] = F[85,x]+F[88,x]
F[85,x] = F[23,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[19,x]*F[84,x]
F[88,x] = F[89,x]
F[89,x] = F[2,x]*F[29,x]*F[62,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{19}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{43}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{23}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{20}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right) F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = -F_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{16}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{40}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{8}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{0}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{19}\! \left(x \right) F_{32}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{0}\! \left(x \right) F_{19}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{30}\! \left(x \right)
F_{40}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{19}\! \left(x \right) F_{20}\! \left(x \right) F_{32}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{74}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{19}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{63}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{2}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{61}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{59}\! \left(x \right)
F_{54}\! \left(x \right) = F_{10}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{54}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{30}\! \left(x \right) F_{5}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{19}\! \left(x \right) F_{52}\! \left(x \right)
F_{61}\! \left(x \right) = F_{0}\! \left(x \right) F_{30}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{50}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{19}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{8}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{19}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{19}\! \left(x \right) F_{32}\! \left(x \right) F_{46}\! \left(x \right)
F_{78}\! \left(x \right) = F_{2}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{19}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{57}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{88}\! \left(x \right)
F_{85}\! \left(x \right) = F_{23}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{19}\! \left(x \right) F_{84}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{2}\! \left(x \right) F_{29}\! \left(x \right) F_{62}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_19(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_19(x)*F_7(x))
Eq(F_7(x), F_43(x) + F_8(x))
Eq(F_8(x), F_23(x) + F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_19(x))
Eq(F_12(x), F_13(x) + F_20(x))
Eq(F_13(x), F_14(x) + F_9(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x) + F_2(x))
Eq(F_16(x), -F_2(x) + F_5(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_19(x)*F_2(x))
Eq(F_19(x), x)
Eq(F_20(x), -F_14(x) + F_21(x))
Eq(F_21(x), F_22(x)/F_19(x))
Eq(F_22(x), F_16(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_19(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_40(x))
Eq(F_26(x), F_27(x) + F_8(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_19(x)*F_29(x))
Eq(F_29(x), F_0(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_0(x)*F_19(x)*F_32(x))
Eq(F_32(x), F_29(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_19(x)*F_35(x))
Eq(F_35(x), F_36(x)/F_19(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_19(x)*F_32(x)*F_38(x))
Eq(F_38(x), F_39(x)/(F_0(x)*F_19(x)))
Eq(F_39(x), F_30(x))
Eq(F_40(x), F_20(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_19(x)*F_20(x)*F_32(x))
Eq(F_43(x), F_44(x) + F_74(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_19(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_63(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_0(x)**2*F_50(x))
Eq(F_50(x), F_51(x)/F_19(x))
Eq(F_51(x), F_2(x))
Eq(F_52(x), F_53(x) + F_61(x))
Eq(F_53(x), F_54(x) + F_59(x))
Eq(F_54(x), F_10(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_19(x)*F_57(x))
Eq(F_57(x), F_54(x) + F_58(x))
Eq(F_58(x), F_30(x)*F_5(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_19(x)*F_52(x))
Eq(F_61(x), F_0(x)*F_30(x)*F_62(x))
Eq(F_62(x), -F_0(x) + F_50(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_65(x) - F_83(x))
Eq(F_65(x), F_66(x)/F_19(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_68(x) - F_78(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_19(x)*F_70(x))
Eq(F_70(x), F_71(x)/F_19(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), -F_4(x) + F_8(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_19(x)*F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_19(x)*F_32(x)*F_46(x))
Eq(F_78(x), F_2(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_19(x)*F_81(x))
Eq(F_81(x), F_57(x) + F_82(x))
Eq(F_82(x), F_2(x)*F_4(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_85(x) + F_88(x))
Eq(F_85(x), F_23(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_19(x)*F_84(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_2(x)*F_29(x)*F_62(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 0]]}]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": 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