02143_02413_02431_20143_20413_20431_24013_24031
Counting sequence:
1, 1, 2, 6, 24, 112, 562, 2926, 15578, 84253, 461242, 2549908, 14211412, 79745508, 450081838, 2552946052, 14543612544, 83166912402, 477181610838, 2746062765924, 15845094030930, 91647577857421, 531238621179010, 3085424647445196, 17952389365423098, 104627601946549283, 610702242526961350, 3569613251565093942, 20891809683421541276, 122420428294303611536, 718155588236979590482, 4217329323643531070436, 24790282381604530726796, 145855848430514129466428, 858895832897190722234320, 5061851702512423832616392, 29854548694843110801477498, 176207892792195228625211173, 1040727535291627765027158866, 6150777306341935130665244364, 36373900004700918791445493246, 215230275755400347862499384975, 1274260391927551993137009251588, 7548191669338948327741305750870, 44734949994803051787908178461814, 265253064953627092177319142733213, 1573526510128986223505621295962554, 9338546874491412305633059106531384, 55445725256792349985221809061689466, 329331149245589501127848803281668011, 1956890122620783815656649490334959856, 11632211942661697554134060688482410438, 69169421633029753786843838287958656882, 411449043388269450145273922526326065455, 2448287885907040667755829292947101222682, 14572973505273979973039210283365742049798, 86769715055879218013176281453076540773756, 516794376175491050725046428297199746120928, 3078878527971769290525558658180503229254416, 18347981232256975440567415284812576790609820, 109370697096208364115057987996709741615672832, 652118978142126219476417156608412012228211640, 3889217743617805632366015098684586998777113042, 23200845239908475934525219543232784168537847552, 138435737838255188802108879096819423649086026032, 826213686464074950536898643187433229130979612874, 4932116608594754720360967732257194310369959214504, 29448843366591461763570306803409839826224182369260, 175871067770667544029340790015501377038748473134732, 1050531859427061337069179407818500397494734504667214, 6276394810154305809428798290705316111355612031718472, 37505513658465928510452438753385528294860945674338904, 224161773787586388858577084413549037532738027489317816, 1340008018883055233660823434115955770067260542978617176, 8011808645296670796608895565235816135390623325514963378, 47910320214191262198192081432720502666458209740144346894, 286550387977980083889817706954220417030538068252233749770, 1714132987977294715121145694198153436138720544862177996117, 10255523748765178375867692324212738188052971306291648177398, 61367622672013613030607937315355326166519751250681113830634, 367271513920306124484452869381028971909040070838137844601144, 2198366571139005384124959008891762771758177535006641909419714, 13160621112747065336105718841800643271997609816587872781266646, 78797894459067418116176259099606913381192894932244620443462304, 471860244200799896590839043988860672391153759076126967991935360, 2825994800208980337312100649928373046090718092658531949424311804, 16927281574783935133216199132302624012511557258087768242756387696, 101405079217117938589661078185743541908627121991093148499157323294, 607557816767245483508810162392581941853137585526524190083841768918, 3640573105415466358648563583571215532415331961328809372543478051425, 21817501003662435533757150468831197801076019128502670852052583352752, 130765223491983178804309145511660592909870201752140798997340463745290, 783845488396519066280804186882349399148144188982731897095026346253566, 4699142188633020985279810457234480728543839835385562161279565483192445, 28174462351039847271720461942063890837255146412639321404183473837503514, 168943176057476768866476208623968658527840337090919341029878783502645224, 1013147569792261740498003091281489895671258831732783251181234820096313402, 6076463492581850864728148614715971763391884506305567056399701760010914451, 36448053367961664810751706607677097989215488789445899693256646827658613536, 218646331764720154162565773891090248912668702990087152647535282462628583910, 1311757763099975947343903526434584607690634347302069438013082141607124838324
Implicit equation for the generating function in Maple syntax:
(3*x-2)*x^3*F(x)^6+6*x^2*(x-1)^2*F(x)^5-x*(13*x^3-6*x^2-9*x+6)*F(x)^4+(30*x^3-32*x^2+6*x+2)*F(x)^3+(-18*x^3+4*x^2+14*x-6)*F(x)^2+3*(3*x-2)*(2*x-1)*F(x)-(3*x-2)*(2*x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(3 x -2\right) x^{3} F \! \left(x \right)^{6}+6 x^{2} \left(x -1\right)^{2} F \! \left(x \right)^{5}-x \left(13 x^{3}-6 x^{2}-9 x +6\right) F \! \left(x \right)^{4}+\left(30 x^{3}-32 x^{2}+6 x +2\right) F \! \left(x \right)^{3}+\left(-18 x^{3}+4 x^{2}+14 x -6\right) F \! \left(x \right)^{2}+3 \left(3 x -2\right) \left(2 x -1\right) F \! \left(x \right)-\left(3 x -2\right) \left(2 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) = 112
a(6) = 562
a(7) = 2926
a(8) = 15578
a(9) = 84253
a(10) = 461242
a(11) = 2549908
a(12) = 14211412
a(13) = 79745508
a(14) = 450081838
a(15) = 2552946052
a(16) = 14543612544
a(17) = 83166912402
a(18) = 477181610838
a(19) = 2746062765924
a(20) = 15845094030930
a(21) = 91647577857421
a(22) = 531238621179010
a(23) = 3085424647445196
a(24) = 17952389365423098
a(25) = 104627601946549283
a(26) = 610702242526961350
a(27) = 3569613251565093942
a(28) = 20891809683421541276
a(29) = 122420428294303611536
a(30) = 718155588236979590482
a(31) = 4217329323643531070436
a(32) = 24790282381604530726796
a(33) = 145855848430514129466428
a(34) = 858895832897190722234320
a(35) = 5061851702512423832616392
a(36) = 29854548694843110801477498
a(37) = 176207892792195228625211173
a(38) = 1040727535291627765027158866
a(39) = 6150777306341935130665244364
a(40) = 36373900004700918791445493246
a(41) = 215230275755400347862499384975
a(42) = 1274260391927551993137009251588
a(43) = 7548191669338948327741305750870
a(44) = 44734949994803051787908178461814
a(45) = 265253064953627092177319142733213
a(46) = 1573526510128986223505621295962554
a(47) = 9338546874491412305633059106531384
a(48) = 55445725256792349985221809061689466
a(49) = 329331149245589501127848803281668011
a(50) = 1956890122620783815656649490334959856
a(51) = 11632211942661697554134060688482410438
a(52) = 69169421633029753786843838287958656882
a(n+53) = 1/19968*(2964226074114754*n^5+678782440049576265*n^4+62172719620912026385*n^3+2847276668471100104145*n^2+65195938985129275543471*n+597121914724689061066830)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+46)-1/6656*(61744646960338*n^5+14436768906368450*n^4+1350164512400992055*n^3+63133496456645700850*n^2+1476012137167766923947*n+13802806500779982114120)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+47)+1/9984*(4840576901722*n^5+1155075720940965*n^4+110246736115408120*n^3+5261061618512995710*n^2+125526029485189744153*n+1197946250427714214080)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+48)-1/4992*(102836271808*n^5+25032426750630*n^4+2437235239038175*n^3+118642460006622345*n^2+2887562270702235292*n+28110036146890642860)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+49)+1/425984*(60491874181498451088551*n^5+12086385348776061653084825*n^4+965982548873697796081549815*n^3+38603488129637769456249832325*n^2+771381454391805474633117347284*n+6165781719724849499820925679660)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+40)-1/638976*(12204212824338224898004*n^5+2498105448866759660437305*n^4+204541478244972737096996110*n^3+8373992071722977580526595205*n^2+171421429826386869182112120316*n+1403685955212515874257764721100)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+41)+1/319488*(738803990063362177991*n^5+154834125310308351686295*n^4+12979856686280282813437760*n^3+544063633573815344312406375*n^2+11402678932437429760885901339*n+95594362990319952225963497700)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+42)-1/159744*(39995229864389552783*n^5+8576820812345864306610*n^4+735709439995816060624745*n^3+31554327498765723671133765*n^2+676682393580312221782550087*n+5804634724339855689509270520)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+43)+1/26624*(640216836621929027*n^5+140404007595939901175*n^4+12316571587482644205290*n^3+540217651612087544771935*n^2+11847234369207933201012023*n+103926216816763797805898310)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+44)-5/26624*(10801437280205748*n^5+2421203002437945951*n^4+217087503293684098932*n^3+9732020711730649980569*n^2+218140551758273639288028*n+1955805032280616673187256)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+45)+1/851968*(4980926822738138989463879*n^5+946395902053748680321081545*n^4+71931052110727477918217577095*n^3+2733707035281782379030896317045*n^2+51949410131708452619664271037996*n+394905725467275371354445081405560)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+38)-1/1277952*(1221205355320307096642029*n^5+238019148633223122808695330*n^4+18557193379886376724590262180*n^3+723437370082824442793113991115*n^2+14101939907118397397123708632996*n+109960588352970760479617148961080)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+39)-1/5111808*(3997616203049382749690509814*n^5+700762401858985513085390974215*n^4+49139633465754539358858176653910*n^3+1723041665643482631224845502105295*n^2+30210900781555391185047127424767346*n+211897991022659425101638674184771460)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+35)+1/2555904*(426300824490033205598141276*n^5+76818094495927912478670200145*n^4+5537310306447940022639203279370*n^3+199587541957676447457716490652815*n^2+3597232100532603397666352918885054*n+25935530978775306142636860127769340)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+36)-1/2555904*(83424235297909456326686417*n^5+15441871812003582792778793685*n^4+1143384007198957022952818654300*n^3+42333087214332525015524119381560*n^2+783726606246080931507550129856978*n+5804130819831183626833544804504340)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+37)+1/20447232*(1001160399155005462104831067702*n^5+160803063610740151857288737380395*n^4+10332054877380071175788192957307685*n^3+331964967826892556340455808304548395*n^2+5333500624274483059185564526897055713*n+34279802452237502476820241511177299330)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+32)-1/3407872*(45599458775363479364624135609*n^5+7546874184190350157394809037765*n^4+499657939151107585091301919384675*n^3+16542004975675220730935262171460180*n^2+273851128505414139745911536212256301*n+1813607341931469527667017542863658470)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+33)+1/1703936*(5744108747435943293983946759*n^5+978777671158577329638689245200*n^4+66717581349053207031194663717135*n^3+2274064338924828613099943852670110*n^2+38759015997310275035333439477692336*n+264266163947401207758608756915334460)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+34)-1/81788928*(121386713111693902563306921240977*n^5+17722550706055345238962381017972240*n^4+1035128385835469440517946789303609560*n^3+30233366809768963083616861585062954435*n^2+441574941905682598206470802292782655988*n+2580115603933950686797583009591743239720)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+29)+1/81788928*(42154354754271710846410412485241*n^5+6359611580026798594941506241128715*n^4+383820128864369617723825287605056325*n^3+11583647702276767771758709749217860495*n^2+174817428959306929022141120643254067344*n+1055448856858205078440190407192839338160)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+30)-1/13631488*(2253610412089793867700669317327*n^5+350970375151194209563774730820485*n^4+21865900919342335697592877943629835*n^3+681210025221625408886348727199485775*n^2+10612380254657533729377727107013881698*n+66138448902261130014612374103318657600)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+31)-1/327155712*(3174475819630998406401720075140686*n^5+432667838533925293378298642290785975*n^4+23591667672431090990693977008155958040*n^3+643273003226808500749444673797840177875*n^2+8771336629918967031662335488061105303204*n+47847693987930032564984725555346969988480)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+27)+1/81788928*(322920507115274101908627663550606*n^5+45578451343330561283928230517628005*n^4+2573597060249963159831074701989725705*n^3+72669121273986999571046118114718835910*n^2+1026098055151375759956524962132964941924*n+5796269305884562715114770575097668334260)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+28)-3/54525952*(2894758972633232694210913121693417*n^5+338586660241393969060025388972014530*n^4+15844148961328404693803409742082151305*n^3+370783083443941216176109954355643398740*n^2+4339332643266941915293748640819262340228*n+20317392128543291400745217614669276978400)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+23)+5/218103808*(3895060665207283878685777651443603*n^5+474379059514050818792930965599922147*n^4+23113888324559966567922693817690837979*n^3+563206097135591169006081045912017023109*n^2+6862920848030820419413960793385998856730*n+33457097289212360901785862590126938684560)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+24)-5/327155712*(3020695856446882481941825839256466*n^5+382478223189390694622873964122388201*n^4+19374810077551934114378773947980318132*n^3+490806267380405451117108391623425266131*n^2+6217637454431896280515989291645675893438*n+31511853752707252912237295161349919760560)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+25)+1/654311424*(14412135337430962080853283034403759*n^5+1894537151853555961098258079450539855*n^4+99633185784153482844986017636222350085*n^3+2620246069360663109325518365574638683105*n^2+34460237386668943751698823119318951692796*n+181310691927760799851598394989572170864960)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+26)-1/327155712*(129508842466323188919494233539370094*n^5+13899797328307430124882756317487762645*n^4+596857296489345740607374905165411141040*n^3+12817249626116432526669581984023100268675*n^2+137651379022079006673865467050889179297426*n+591448005887673661014839420156402441457000)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+21)+1/109051904*(28542745382375085431450900963764559*n^5+3200920262562707790994368698870398425*n^4+143615467662413070725075779993376399425*n^3+3222438807393508466746167844084135736095*n^2+36159707331631228958970636203926111188696*n+162334707130029598760290598830997778233120)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+22)+1/327155712*(268488150331272093523701361145946421*n^5+24936864825807895275206941234407235035*n^4+926678083927739174631054992442801774415*n^3+17222366664039173243451108626486759059605*n^2+160077384837317438621177550735605326471084*n+595287008047973853404097036783564825635760)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+18)-1/327155712*(229703375767717602914117258369640779*n^5+22440945767082511055784444960131128575*n^4+877161455810158986244522277314439528735*n^3+17147082713761227062562374865565643894145*n^2+167637326949757919430025200497176853027366*n+655704583114223989484368809924242913316800)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+19)+3/218103808*(40008950201067261521823088129277549*n^5+4101354914474141230381346686610473645*n^4+168211759808401872879455340351641438785*n^3+3450267466528279426975657346658041332475*n^2+35392802364371058407002957446439666940386*n+145254993428137731711275746069704374793480)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+20)-1/27262976*(20665954943608266114592965382998874*n^5+1620379355100505533738813515860688740*n^4+50835143321901543661042936687119288725*n^3+797624462319855721772097865718212029125*n^2+6259081059630006326367644559119586753246*n+19650825177174914256132580386856199156640)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+15)+1/163577856*(139835882989736713831170238644495983*n^5+11639522404152992682178303492326381585*n^4+387643785782000952198749248438954468475*n^3+6456764271257391402648840774216496594635*n^2+53786648104012600768314931814057185844282*n+179264472828115013024748907696255805514600)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+16)-1/54525952*(47819639587855549714289836266778701*n^5+4210995156350317849766991270277211815*n^4+148367586251873992919181158868323342665*n^3+2614413717436512265089958593941743771235*n^2+23040157586838916719883422592294210187624*n+81237589299772468086753643712156309603640)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+17)+9/3407872*(109767025107387071519025139058566*n^5+7010092507718169123182586314104995*n^4+179132738181925042381606030173713485*n^3+2289359829126236855976632239101178815*n^2+14632530408827464109315148793917916204*n+37416190627289619489521566955453416530)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+12)-9/6815744*(335533868506189267623718939340814*n^5+23059173328424348146248618725040080*n^4+634083299108884058987760681424113995*n^3+8720430785885390192001175387189210315*n^2+59979414676317339691647399670365236761*n+165048921534812893328676247154969087250)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+13)+3/13631488*(2769902621138651756537903128445562*n^5+203785110616870281766247207187053215*n^4+5998894305171277959624243334056730310*n^3+88319914672975024362838075664780813570*n^2+650312835081847439857291530506269123483*n+1915753672883899179447291288878429412030)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+14)-243/425984*(72134159081467067073911813736*n^5+3547330245280331933494203338670*n^4+69802250685564818336829893969275*n^3+686915574427836641504127375410565*n^2+3380284388879906227929749769356564*n+6653654578990292836282905316551540)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+9)+405/851968*(186893432743936759593936118206*n^5+10109492529176618231526209147493*n^4+218811922967466966268169393828272*n^3+2368595080673553909399632262136803*n^2+12821863264978274145001366018214345*n+27765464511948481444385054829888102)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+10)-27/1703936*(10726593455466535290929982109102*n^5+632730433627131715101480466904270*n^4+14934092379285171913487775342234735*n^3+176288337068020129980220908722393965*n^2+1040697396065807549518309522036122623*n+2457781791606866190780960287764551690)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+11)+6561/26624*(7400338090551525791762031*n^5+253916618626066351458595650*n^4+3485362218759881375681817775*n^3+23916900786808807254290383860*n^2+82023731073648492548866209584*n+112441270048148598225772075560)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+6)-2187/53248*(145010734573838746452107832*n^5+5696458119127866748135262115*n^4+89534205220452713994829367690*n^3+703670553556252027995120125355*n^2+2764749352157571785128305632548*n+4343619698566060369163997700200)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+7)+729/212992*(4898375758437829734795371061*n^5+216703679226314879005088759610*n^4+3836030277163816809072091220480*n^3+33957886050308682978433487278905*n^2+150305551104409447686340280005534*n+266078888965805590675147273259520)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+8)-885735/832*(16517366109227422132*n^5+321082279477027080543*n^4+2489005916158610100332*n^3+9609311188394108115297*n^2+18460990765608112501518*n+14108382958336155825588)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+3)+295245/3328*(1150412606997915320121*n^5+28037477364396616733562*n^4+273039429949924879438663*n^3+1327303891403587373902782*n^2+3219106047458731530165140*n+3114512879225224771028952)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+4)-19683/6656*(160216024156245105985422*n^5+4700057503083087753117765*n^4+55139660165765538576179590*n^3+323237995233961918467534435*n^2+946475813831042922249250508*n+1107025595903177960981785380)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+5)+2657205/416*(n+2)*(356986057911353707*n^4+4482989967309818322*n^3+21046912309082360507*n^2+43716688926478485480*n+33850197454932964854)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+2)-2176250895/8*(2*n+3)*(n+2)*(n+1)*(364321627307*n^2+1910123893888*n+2519090134676)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n+1)+8660943380034366525/4*n*(2*n+3)*(2*n+1)*(n+2)*(n+1)/(2*n+105)/(n+54)/(n+53)/(n+52)/(n+51)*a(n)+1/52*(13558*n^2+1379427*n+35081610)/(n+54)/(2*n+105)*a(n+52)+1/416*(284098108*n^4+56025496602*n^3+4143089481288*n^2+136166567340327*n+1678178564080910)/(n+52)/(n+53)/(n+54)/(2*n+105)*a(n+50)-1/208*(3443408*n^3+516436636*n^2+25817459551*n+430207453430)/(n+53)/(n+54)/(2*n+105)*a(n+51), n >= 53
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 24
a \! \left(5\right) = 112
a \! \left(6\right) = 562
a \! \left(7\right) = 2926
a \! \left(8\right) = 15578
a \! \left(9\right) = 84253
a \! \left(10\right) = 461242
a \! \left(11\right) = 2549908
a \! \left(12\right) = 14211412
a \! \left(13\right) = 79745508
a \! \left(14\right) = 450081838
a \! \left(15\right) = 2552946052
a \! \left(16\right) = 14543612544
a \! \left(17\right) = 83166912402
a \! \left(18\right) = 477181610838
a \! \left(19\right) = 2746062765924
a \! \left(20\right) = 15845094030930
a \! \left(21\right) = 91647577857421
a \! \left(22\right) = 531238621179010
a \! \left(23\right) = 3085424647445196
a \! \left(24\right) = 17952389365423098
a \! \left(25\right) = 104627601946549283
a \! \left(26\right) = 610702242526961350
a \! \left(27\right) = 3569613251565093942
a \! \left(28\right) = 20891809683421541276
a \! \left(29\right) = 122420428294303611536
a \! \left(30\right) = 718155588236979590482
a \! \left(31\right) = 4217329323643531070436
a \! \left(32\right) = 24790282381604530726796
a \! \left(33\right) = 145855848430514129466428
a \! \left(34\right) = 858895832897190722234320
a \! \left(35\right) = 5061851702512423832616392
a \! \left(36\right) = 29854548694843110801477498
a \! \left(37\right) = 176207892792195228625211173
a \! \left(38\right) = 1040727535291627765027158866
a \! \left(39\right) = 6150777306341935130665244364
a \! \left(40\right) = 36373900004700918791445493246
a \! \left(41\right) = 215230275755400347862499384975
a \! \left(42\right) = 1274260391927551993137009251588
a \! \left(43\right) = 7548191669338948327741305750870
a \! \left(44\right) = 44734949994803051787908178461814
a \! \left(45\right) = 265253064953627092177319142733213
a \! \left(46\right) = 1573526510128986223505621295962554
a \! \left(47\right) = 9338546874491412305633059106531384
a \! \left(48\right) = 55445725256792349985221809061689466
a \! \left(49\right) = 329331149245589501127848803281668011
a \! \left(50\right) = 1956890122620783815656649490334959856
a \! \left(51\right) = 11632211942661697554134060688482410438
a \! \left(52\right) = 69169421633029753786843838287958656882
a \! \left(n +53\right) = \frac{\left(2964226074114754 n^{5}+678782440049576265 n^{4}+62172719620912026385 n^{3}+2847276668471100104145 n^{2}+65195938985129275543471 n +597121914724689061066830\right) a \! \left(n +46\right)}{19968 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(61744646960338 n^{5}+14436768906368450 n^{4}+1350164512400992055 n^{3}+63133496456645700850 n^{2}+1476012137167766923947 n +13802806500779982114120\right) a \! \left(n +47\right)}{6656 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(4840576901722 n^{5}+1155075720940965 n^{4}+110246736115408120 n^{3}+5261061618512995710 n^{2}+125526029485189744153 n +1197946250427714214080\right) a \! \left(n +48\right)}{9984 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(102836271808 n^{5}+25032426750630 n^{4}+2437235239038175 n^{3}+118642460006622345 n^{2}+2887562270702235292 n +28110036146890642860\right) a \! \left(n +49\right)}{4992 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(60491874181498451088551 n^{5}+12086385348776061653084825 n^{4}+965982548873697796081549815 n^{3}+38603488129637769456249832325 n^{2}+771381454391805474633117347284 n +6165781719724849499820925679660\right) a \! \left(n +40\right)}{425984 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(12204212824338224898004 n^{5}+2498105448866759660437305 n^{4}+204541478244972737096996110 n^{3}+8373992071722977580526595205 n^{2}+171421429826386869182112120316 n +1403685955212515874257764721100\right) a \! \left(n +41\right)}{638976 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(738803990063362177991 n^{5}+154834125310308351686295 n^{4}+12979856686280282813437760 n^{3}+544063633573815344312406375 n^{2}+11402678932437429760885901339 n +95594362990319952225963497700\right) a \! \left(n +42\right)}{319488 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(39995229864389552783 n^{5}+8576820812345864306610 n^{4}+735709439995816060624745 n^{3}+31554327498765723671133765 n^{2}+676682393580312221782550087 n +5804634724339855689509270520\right) a \! \left(n +43\right)}{159744 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(640216836621929027 n^{5}+140404007595939901175 n^{4}+12316571587482644205290 n^{3}+540217651612087544771935 n^{2}+11847234369207933201012023 n +103926216816763797805898310\right) a \! \left(n +44\right)}{26624 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{5 \left(10801437280205748 n^{5}+2421203002437945951 n^{4}+217087503293684098932 n^{3}+9732020711730649980569 n^{2}+218140551758273639288028 n +1955805032280616673187256\right) a \! \left(n +45\right)}{26624 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(4980926822738138989463879 n^{5}+946395902053748680321081545 n^{4}+71931052110727477918217577095 n^{3}+2733707035281782379030896317045 n^{2}+51949410131708452619664271037996 n +394905725467275371354445081405560\right) a \! \left(n +38\right)}{851968 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(1221205355320307096642029 n^{5}+238019148633223122808695330 n^{4}+18557193379886376724590262180 n^{3}+723437370082824442793113991115 n^{2}+14101939907118397397123708632996 n +109960588352970760479617148961080\right) a \! \left(n +39\right)}{1277952 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(3997616203049382749690509814 n^{5}+700762401858985513085390974215 n^{4}+49139633465754539358858176653910 n^{3}+1723041665643482631224845502105295 n^{2}+30210900781555391185047127424767346 n +211897991022659425101638674184771460\right) a \! \left(n +35\right)}{5111808 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(426300824490033205598141276 n^{5}+76818094495927912478670200145 n^{4}+5537310306447940022639203279370 n^{3}+199587541957676447457716490652815 n^{2}+3597232100532603397666352918885054 n +25935530978775306142636860127769340\right) a \! \left(n +36\right)}{2555904 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(83424235297909456326686417 n^{5}+15441871812003582792778793685 n^{4}+1143384007198957022952818654300 n^{3}+42333087214332525015524119381560 n^{2}+783726606246080931507550129856978 n +5804130819831183626833544804504340\right) a \! \left(n +37\right)}{2555904 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(1001160399155005462104831067702 n^{5}+160803063610740151857288737380395 n^{4}+10332054877380071175788192957307685 n^{3}+331964967826892556340455808304548395 n^{2}+5333500624274483059185564526897055713 n +34279802452237502476820241511177299330\right) a \! \left(n +32\right)}{20447232 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(45599458775363479364624135609 n^{5}+7546874184190350157394809037765 n^{4}+499657939151107585091301919384675 n^{3}+16542004975675220730935262171460180 n^{2}+273851128505414139745911536212256301 n +1813607341931469527667017542863658470\right) a \! \left(n +33\right)}{3407872 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(5744108747435943293983946759 n^{5}+978777671158577329638689245200 n^{4}+66717581349053207031194663717135 n^{3}+2274064338924828613099943852670110 n^{2}+38759015997310275035333439477692336 n +264266163947401207758608756915334460\right) a \! \left(n +34\right)}{1703936 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(121386713111693902563306921240977 n^{5}+17722550706055345238962381017972240 n^{4}+1035128385835469440517946789303609560 n^{3}+30233366809768963083616861585062954435 n^{2}+441574941905682598206470802292782655988 n +2580115603933950686797583009591743239720\right) a \! \left(n +29\right)}{81788928 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(42154354754271710846410412485241 n^{5}+6359611580026798594941506241128715 n^{4}+383820128864369617723825287605056325 n^{3}+11583647702276767771758709749217860495 n^{2}+174817428959306929022141120643254067344 n +1055448856858205078440190407192839338160\right) a \! \left(n +30\right)}{81788928 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(2253610412089793867700669317327 n^{5}+350970375151194209563774730820485 n^{4}+21865900919342335697592877943629835 n^{3}+681210025221625408886348727199485775 n^{2}+10612380254657533729377727107013881698 n +66138448902261130014612374103318657600\right) a \! \left(n +31\right)}{13631488 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(3174475819630998406401720075140686 n^{5}+432667838533925293378298642290785975 n^{4}+23591667672431090990693977008155958040 n^{3}+643273003226808500749444673797840177875 n^{2}+8771336629918967031662335488061105303204 n +47847693987930032564984725555346969988480\right) a \! \left(n +27\right)}{327155712 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(322920507115274101908627663550606 n^{5}+45578451343330561283928230517628005 n^{4}+2573597060249963159831074701989725705 n^{3}+72669121273986999571046118114718835910 n^{2}+1026098055151375759956524962132964941924 n +5796269305884562715114770575097668334260\right) a \! \left(n +28\right)}{81788928 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{3 \left(2894758972633232694210913121693417 n^{5}+338586660241393969060025388972014530 n^{4}+15844148961328404693803409742082151305 n^{3}+370783083443941216176109954355643398740 n^{2}+4339332643266941915293748640819262340228 n +20317392128543291400745217614669276978400\right) a \! \left(n +23\right)}{54525952 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{5 \left(3895060665207283878685777651443603 n^{5}+474379059514050818792930965599922147 n^{4}+23113888324559966567922693817690837979 n^{3}+563206097135591169006081045912017023109 n^{2}+6862920848030820419413960793385998856730 n +33457097289212360901785862590126938684560\right) a \! \left(n +24\right)}{218103808 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{5 \left(3020695856446882481941825839256466 n^{5}+382478223189390694622873964122388201 n^{4}+19374810077551934114378773947980318132 n^{3}+490806267380405451117108391623425266131 n^{2}+6217637454431896280515989291645675893438 n +31511853752707252912237295161349919760560\right) a \! \left(n +25\right)}{327155712 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(14412135337430962080853283034403759 n^{5}+1894537151853555961098258079450539855 n^{4}+99633185784153482844986017636222350085 n^{3}+2620246069360663109325518365574638683105 n^{2}+34460237386668943751698823119318951692796 n +181310691927760799851598394989572170864960\right) a \! \left(n +26\right)}{654311424 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(129508842466323188919494233539370094 n^{5}+13899797328307430124882756317487762645 n^{4}+596857296489345740607374905165411141040 n^{3}+12817249626116432526669581984023100268675 n^{2}+137651379022079006673865467050889179297426 n +591448005887673661014839420156402441457000\right) a \! \left(n +21\right)}{327155712 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(28542745382375085431450900963764559 n^{5}+3200920262562707790994368698870398425 n^{4}+143615467662413070725075779993376399425 n^{3}+3222438807393508466746167844084135736095 n^{2}+36159707331631228958970636203926111188696 n +162334707130029598760290598830997778233120\right) a \! \left(n +22\right)}{109051904 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(268488150331272093523701361145946421 n^{5}+24936864825807895275206941234407235035 n^{4}+926678083927739174631054992442801774415 n^{3}+17222366664039173243451108626486759059605 n^{2}+160077384837317438621177550735605326471084 n +595287008047973853404097036783564825635760\right) a \! \left(n +18\right)}{327155712 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(229703375767717602914117258369640779 n^{5}+22440945767082511055784444960131128575 n^{4}+877161455810158986244522277314439528735 n^{3}+17147082713761227062562374865565643894145 n^{2}+167637326949757919430025200497176853027366 n +655704583114223989484368809924242913316800\right) a \! \left(n +19\right)}{327155712 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{3 \left(40008950201067261521823088129277549 n^{5}+4101354914474141230381346686610473645 n^{4}+168211759808401872879455340351641438785 n^{3}+3450267466528279426975657346658041332475 n^{2}+35392802364371058407002957446439666940386 n +145254993428137731711275746069704374793480\right) a \! \left(n +20\right)}{218103808 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(20665954943608266114592965382998874 n^{5}+1620379355100505533738813515860688740 n^{4}+50835143321901543661042936687119288725 n^{3}+797624462319855721772097865718212029125 n^{2}+6259081059630006326367644559119586753246 n +19650825177174914256132580386856199156640\right) a \! \left(n +15\right)}{27262976 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(139835882989736713831170238644495983 n^{5}+11639522404152992682178303492326381585 n^{4}+387643785782000952198749248438954468475 n^{3}+6456764271257391402648840774216496594635 n^{2}+53786648104012600768314931814057185844282 n +179264472828115013024748907696255805514600\right) a \! \left(n +16\right)}{163577856 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{\left(47819639587855549714289836266778701 n^{5}+4210995156350317849766991270277211815 n^{4}+148367586251873992919181158868323342665 n^{3}+2614413717436512265089958593941743771235 n^{2}+23040157586838916719883422592294210187624 n +81237589299772468086753643712156309603640\right) a \! \left(n +17\right)}{54525952 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{9 \left(109767025107387071519025139058566 n^{5}+7010092507718169123182586314104995 n^{4}+179132738181925042381606030173713485 n^{3}+2289359829126236855976632239101178815 n^{2}+14632530408827464109315148793917916204 n +37416190627289619489521566955453416530\right) a \! \left(n +12\right)}{3407872 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{9 \left(335533868506189267623718939340814 n^{5}+23059173328424348146248618725040080 n^{4}+634083299108884058987760681424113995 n^{3}+8720430785885390192001175387189210315 n^{2}+59979414676317339691647399670365236761 n +165048921534812893328676247154969087250\right) a \! \left(n +13\right)}{6815744 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{3 \left(2769902621138651756537903128445562 n^{5}+203785110616870281766247207187053215 n^{4}+5998894305171277959624243334056730310 n^{3}+88319914672975024362838075664780813570 n^{2}+650312835081847439857291530506269123483 n +1915753672883899179447291288878429412030\right) a \! \left(n +14\right)}{13631488 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{243 \left(72134159081467067073911813736 n^{5}+3547330245280331933494203338670 n^{4}+69802250685564818336829893969275 n^{3}+686915574427836641504127375410565 n^{2}+3380284388879906227929749769356564 n +6653654578990292836282905316551540\right) a \! \left(n +9\right)}{425984 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{405 \left(186893432743936759593936118206 n^{5}+10109492529176618231526209147493 n^{4}+218811922967466966268169393828272 n^{3}+2368595080673553909399632262136803 n^{2}+12821863264978274145001366018214345 n +27765464511948481444385054829888102\right) a \! \left(n +10\right)}{851968 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{27 \left(10726593455466535290929982109102 n^{5}+632730433627131715101480466904270 n^{4}+14934092379285171913487775342234735 n^{3}+176288337068020129980220908722393965 n^{2}+1040697396065807549518309522036122623 n +2457781791606866190780960287764551690\right) a \! \left(n +11\right)}{1703936 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{6561 \left(7400338090551525791762031 n^{5}+253916618626066351458595650 n^{4}+3485362218759881375681817775 n^{3}+23916900786808807254290383860 n^{2}+82023731073648492548866209584 n +112441270048148598225772075560\right) a \! \left(n +6\right)}{26624 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{2187 \left(145010734573838746452107832 n^{5}+5696458119127866748135262115 n^{4}+89534205220452713994829367690 n^{3}+703670553556252027995120125355 n^{2}+2764749352157571785128305632548 n +4343619698566060369163997700200\right) a \! \left(n +7\right)}{53248 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{729 \left(4898375758437829734795371061 n^{5}+216703679226314879005088759610 n^{4}+3836030277163816809072091220480 n^{3}+33957886050308682978433487278905 n^{2}+150305551104409447686340280005534 n +266078888965805590675147273259520\right) a \! \left(n +8\right)}{212992 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{885735 \left(16517366109227422132 n^{5}+321082279477027080543 n^{4}+2489005916158610100332 n^{3}+9609311188394108115297 n^{2}+18460990765608112501518 n +14108382958336155825588\right) a \! \left(n +3\right)}{832 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{295245 \left(1150412606997915320121 n^{5}+28037477364396616733562 n^{4}+273039429949924879438663 n^{3}+1327303891403587373902782 n^{2}+3219106047458731530165140 n +3114512879225224771028952\right) a \! \left(n +4\right)}{3328 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{19683 \left(160216024156245105985422 n^{5}+4700057503083087753117765 n^{4}+55139660165765538576179590 n^{3}+323237995233961918467534435 n^{2}+946475813831042922249250508 n +1107025595903177960981785380\right) a \! \left(n +5\right)}{6656 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{2657205 \left(n +2\right) \left(356986057911353707 n^{4}+4482989967309818322 n^{3}+21046912309082360507 n^{2}+43716688926478485480 n +33850197454932964854\right) a \! \left(n +2\right)}{416 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}-\frac{2176250895 \left(2 n +3\right) \left(n +2\right) \left(n +1\right) \left(364321627307 n^{2}+1910123893888 n +2519090134676\right) a \! \left(n +1\right)}{8 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{8660943380034366525 n \left(2 n +3\right) \left(2 n +1\right) \left(n +2\right) \left(n +1\right) a \! \left(n \right)}{4 \left(2 n +105\right) \left(n +54\right) \left(n +53\right) \left(n +52\right) \left(n +51\right)}+\frac{\left(13558 n^{2}+1379427 n +35081610\right) a \! \left(n +52\right)}{52 \left(n +54\right) \left(2 n +105\right)}+\frac{\left(284098108 n^{4}+56025496602 n^{3}+4143089481288 n^{2}+136166567340327 n +1678178564080910\right) a \! \left(n +50\right)}{416 \left(n +52\right) \left(n +53\right) \left(n +54\right) \left(2 n +105\right)}-\frac{\left(3443408 n^{3}+516436636 n^{2}+25817459551 n +430207453430\right) a \! \left(n +51\right)}{208 \left(n +53\right) \left(n +54\right) \left(2 n +105\right)}, \quad n \geq 53
Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24166/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[12,x]+F[8,x]
F[8,x] = F[0,x]*F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[0,x]*F[11,x]*F[14,x]*F[48,x]
F[14,x] = 1/F[11,x]/F[48,x]*F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[11,x]*F[17,x]*F[48,x]
F[17,x] = F[18,x]+F[81,x]
F[18,x] = F[19,x]+F[80,x]
F[19,x] = F[0,x]+F[20,x]
F[20,x] = 1/F[0,x]/F[11,x]/F[48,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]*F[14,x]*F[23,x]
F[24,x,k[0]] = F[23,x]*F[28,x]*F[44,x,k[0]]*F[47,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[26,x,k[0]] = F[25,x,k[0]]+F[78,x]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[0,x]*F[11,x]*F[28,x]*F[44,x,k[0]]*F[48,x]
F[28,x] = F[1,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]*F[31,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[11,x]*F[32,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[37,x]
F[37,x] = F[11,x]*F[38,x]
F[38,x] = F[1,x]+F[36,x]
F[39,x] = F[40,x]+F[41,x]+F[43,x]
F[40,x] = 0
F[41,x] = F[11,x]*F[42,x]
F[42,x] = F[33,x]+F[39,x]
F[43,x] = F[11,x]*F[35,x]
F[44,x,k[0]] = F[1,x]+F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[44,x,k[0]]*F[47,x,k[0]]
F[47,x,k[0]] = k[0]*x
F[48,x] = F[49,x]+F[58,x]
F[49,x] = F[50,x]+F[53,x]
F[50,x] = F[1,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[11,x]*F[49,x]
F[53,x] = F[54,x]
F[54,x] = F[11,x]*F[49,x]*F[55,x]
F[55,x] = F[32,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[55,x]^2*F[11,x]
F[58,x] = F[11,x]*F[59,x]
F[59,x] = F[60,x]+F[65,x]+F[76,x]
F[60,x] = F[61,x]+F[64,x]
F[61,x] = F[1,x]+F[62,x]+F[63,x]
F[62,x] = F[11,x]*F[61,x]
F[63,x] = F[11,x]*F[48,x]
F[64,x] = F[11,x]*F[59,x]
F[65,x] = F[66,x]
F[66,x] = F[11,x]*F[59,x]*F[67,x]
F[67,x] = F[55,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[11,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]+F[74,x]
F[71,x] = F[31,x]*F[32,x]
F[72,x] = F[73,x]
F[73,x] = F[11,x]*F[67,x]*F[70,x]
F[74,x] = F[75,x]
F[75,x] = F[11,x]*F[55,x]*F[70,x]
F[76,x] = F[77,x]
F[77,x] = F[11,x]*F[49,x]*F[70,x]
F[78,x] = F[79,x]
F[79,x] = F[0,x]*F[11,x]*F[28,x]*F[48,x]
F[80,x] = F[20,x]
F[81,x] = -F[87,x]+F[82,x]
F[82,x] = 1/F[11,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = -F[0,x]+F[85,x]
F[85,x] = 1/F[11,x]*F[86,x]
F[86,x] = F[2,x]
F[87,x] = F[85,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[11,x]*F[90,x]
F[90,x] = 1/F[11,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[2,x]*F[85,x]
F[94,x] = F[95,x]
F[95,x] = F[11,x]*F[96,x]*F[98,x]
F[96,x] = 1/F[11,x]*F[97,x]
F[97,x] = F[81,x]
F[98,x] = F[51,x]+F[99,x]
F[99,x] = F[100,x]+F[40,x]+F[62,x]
F[100,x] = F[101,x]*F[11,x]
F[101,x] = F[58,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_{11}\! \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_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{48}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{11}\! \left(x \right) F_{48}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{48}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{81}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{80}\! \left(x \right)
F_{19}\! \left(x \right) = F_{0}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{48}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{23}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{23}\! \left(x \right) F_{28}\! \left(x \right) F_{44}\! \left(x , y\right) F_{47}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{78}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{28}\! \left(x \right) F_{44}\! \left(x , y\right) F_{48}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = 0
F_{41}\! \left(x \right) = F_{11}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{33}\! \left(x \right)+F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{11}\! \left(x \right) F_{35}\! \left(x \right)
F_{44}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = y x
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{58}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{50}\! \left(x \right) = F_{1}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{11}\! \left(x \right) F_{49}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{11}\! \left(x \right) F_{49}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{32}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{55} \left(x \right)^{2} F_{11}\! \left(x \right)
F_{58}\! \left(x \right) = F_{11}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{65}\! \left(x \right)+F_{76}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{61}\! \left(x \right) = F_{1}\! \left(x \right)+F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right) F_{61}\! \left(x \right)
F_{63}\! \left(x \right) = F_{11}\! \left(x \right) F_{48}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right) F_{59}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{11}\! \left(x \right) F_{59}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{55}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{11}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{71}\! \left(x \right) = F_{31}\! \left(x \right) F_{32}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{11}\! \left(x \right) F_{67}\! \left(x \right) F_{70}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{11}\! \left(x \right) F_{55}\! \left(x \right) F_{70}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{11}\! \left(x \right) F_{49}\! \left(x \right) F_{70}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{28}\! \left(x \right) F_{48}\! \left(x \right)
F_{80}\! \left(x \right) = F_{20}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{87}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{2}\! \left(x \right)
F_{87}\! \left(x \right) = F_{85}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{2}\! \left(x \right) F_{85}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{11}\! \left(x \right) F_{96}\! \left(x \right) F_{98}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{81}\! \left(x \right)
F_{98}\! \left(x \right) = F_{51}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{40}\! \left(x \right)+F_{62}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{11}\! \left(x \right)
F_{101}\! \left(x \right) = F_{58}\! \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_11(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_11(x)*F_7(x))
Eq(F_7(x), F_12(x) + F_8(x))
Eq(F_8(x), F_0(x)*F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_0(x)*F_11(x)*F_14(x)*F_48(x))
Eq(F_14(x), F_15(x)/(F_11(x)*F_48(x)))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_11(x)*F_17(x)*F_48(x))
Eq(F_17(x), F_18(x) + F_81(x))
Eq(F_18(x), F_19(x) + F_80(x))
Eq(F_19(x), F_0(x) + F_20(x))
Eq(F_20(x), F_21(x)/(F_0(x)*F_11(x)*F_48(x)))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)*F_14(x)*F_23(x))
Eq(F_24(x, k_0), F_23(x)*F_28(x)*F_44(x, k_0)*F_47(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_26(x, k_0), F_25(x, k_0) + F_78(x))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_0(x)*F_11(x)*F_28(x)*F_44(x, k_0)*F_48(x))
Eq(F_28(x), F_1(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_11(x)*F_32(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_11(x)*F_38(x))
Eq(F_38(x), F_1(x) + F_36(x))
Eq(F_39(x), F_40(x) + F_41(x) + F_43(x))
Eq(F_40(x), 0)
Eq(F_41(x), F_11(x)*F_42(x))
Eq(F_42(x), F_33(x) + F_39(x))
Eq(F_43(x), F_11(x)*F_35(x))
Eq(F_44(x, k_0), F_1(x) + F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_44(x, k_0)*F_47(x, k_0))
Eq(F_47(x, k_0), k_0*x)
Eq(F_48(x), F_49(x) + F_58(x))
Eq(F_49(x), F_50(x) + F_53(x))
Eq(F_50(x), F_1(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_11(x)*F_49(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_11(x)*F_49(x)*F_55(x))
Eq(F_55(x), F_32(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_11(x)*F_55(x)**2)
Eq(F_58(x), F_11(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_65(x) + F_76(x))
Eq(F_60(x), F_61(x) + F_64(x))
Eq(F_61(x), F_1(x) + F_62(x) + F_63(x))
Eq(F_62(x), F_11(x)*F_61(x))
Eq(F_63(x), F_11(x)*F_48(x))
Eq(F_64(x), F_11(x)*F_59(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_11(x)*F_59(x)*F_67(x))
Eq(F_67(x), F_55(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_11(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x) + F_74(x))
Eq(F_71(x), F_31(x)*F_32(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_11(x)*F_67(x)*F_70(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_11(x)*F_55(x)*F_70(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_11(x)*F_49(x)*F_70(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_0(x)*F_11(x)*F_28(x)*F_48(x))
Eq(F_80(x), F_20(x))
Eq(F_81(x), F_82(x) - F_87(x))
Eq(F_82(x), F_83(x)/F_11(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), -F_0(x) + F_85(x))
Eq(F_85(x), F_86(x)/F_11(x))
Eq(F_86(x), F_2(x))
Eq(F_87(x), F_85(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_11(x)*F_90(x))
Eq(F_90(x), F_91(x)/F_11(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_2(x)*F_85(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_11(x)*F_96(x)*F_98(x))
Eq(F_96(x), F_97(x)/F_11(x))
Eq(F_97(x), F_81(x))
Eq(F_98(x), F_51(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_40(x) + F_62(x))
Eq(F_100(x), F_101(x)*F_11(x))
Eq(F_101(x), F_58(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "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, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "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, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 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, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "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": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "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, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "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, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 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, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "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, 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2]]}, {"patt": [1, 0], "pos": [[1, 7], [1, 7]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[3, 4], [3, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 6], [0, 6], [0, 6]]}, {"patt": [0, 2, 1], "pos": [[2, 5], [2, 5], [2, 5]]}, {"patt": [0, 2, 1], "pos": [[2, 5], [2, 5], [3, 5]]}, {"patt": [0, 2, 1], "pos": [[2, 5], [3, 5], [3, 5]]}, {"patt": [0, 2, 1], "pos": [[3, 5], [3, 5], [3, 5]]}], "requirements": [[{"patt": [0], "pos": [[1, 7]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": 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true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 6]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 5]]}, {"patt": [0], "pos": [[3, 6]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[2, 6], [2, 6]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 6], [2, 6]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 5], [0, 5], [0, 5]]}, {"patt": [0, 2, 1], "pos": [[0, 5], [0, 5], [1, 5]]}, {"patt": [0, 2, 1], "pos": [[0, 5], [1, 5], [1, 5]]}, {"patt": [0, 2, 1], "pos": [[1, 5], [1, 5], [1, 5]]}, {"patt": [0, 2, 1], "pos": [[3, 4], [3, 4], [3, 4]]}], "requirements": [[{"patt": [0], "pos": [[2, 6]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 3], [3, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [3, 3]]}, {"patt": [0, 1], "pos": [[2, 4], [2, 4]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[2, 4], [2, 4]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 3], [3, 3], [3, 3]]}], "requirements": [[{"patt": [0], "pos": [[2, 4]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 4], [2, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [2, 4], [2, 4]]}, {"patt": [0, 2, 1], "pos": [[2, 4], [2, 4], [2, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: row_and_col_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24167/
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[7,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[8,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0]]*F[7,x]
F[6,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[7,x] = x
F[8,x,k[0]] = F[17,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,1,k[0]]
F[10,x,k[0],k[1]] = F[11,x,k[0]*k[1],k[1]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[18,x,k[0],k[1]]+F[24,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[7,x]
F[13,x,k[0],k[1]] = (F[14,x,k[0]]*k[0]-F[14,x,k[1]]*k[1])/(-k[1]+k[0])
F[14,x,k[0]] = F[15,x,k[0]]+F[3,x]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[0,x]*F[14,x,k[0]]*F[17,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0],k[1]] = F[17,x,k[0]]*F[19,x,k[0],k[1]]
F[19,x,k[0],k[1]] = (F[20,x,k[0],1]*k[0]-F[20,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1]] = F[1,x]+F[21,x,k[0],k[1]]+F[22,x,k[0],k[1]]+F[23,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[12,x,k[0],k[0]*k[1]]
F[22,x,k[0],k[1]] = F[18,x,k[0],k[0]*k[1]]
F[23,x,k[0],k[1]] = F[17,x,k[1]]*F[20,x,k[0],k[1]]
F[24,x,k[0],k[1]] = F[17,x,k[1]]*F[25,x,k[0],k[1]]
F[25,x,k[0],k[1]] = (-F[10,x,1,k[1]]*k[1]+F[10,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{5}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y\right) = -\frac{-y F_{4}\! \left(x , y\right)+F_{4}\! \left(x , 1\right)}{-1+y}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , 1, y\right)
F_{10}\! \left(x , y , z\right) = F_{11}\! \left(x , y z , z\right)
F_{11}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{7}\! \left(x \right)
F_{13}\! \left(x , y , z\right) = \frac{y F_{14}\! \left(x , y\right)-z F_{14}\! \left(x , z\right)}{-z +y}
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{3}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y , z\right) = F_{17}\! \left(x , y\right) F_{19}\! \left(x , y , z\right)
F_{19}\! \left(x , y , z\right) = \frac{y F_{20}\! \left(x , y , 1\right)-z F_{20}\! \left(x , y , \frac{z}{y}\right)}{-z +y}
F_{20}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{12}\! \left(x , y , y z \right)
F_{22}\! \left(x , y , z\right) = F_{18}\! \left(x , y , y z \right)
F_{23}\! \left(x , y , z\right) = F_{17}\! \left(x , z\right) F_{20}\! \left(x , y , z\right)
F_{24}\! \left(x , y , z\right) = F_{17}\! \left(x , z\right) F_{25}\! \left(x , y , z\right)
F_{25}\! \left(x , y , z\right) = -\frac{z F_{10}\! \left(x , 1, z\right)-y F_{10}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
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)*F_7(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0)*F_7(x))
Eq(F_6(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_7(x), x)
Eq(F_8(x, k_0), F_17(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, 1, k_0))
Eq(F_10(x, k_0, k_1), F_11(x, k_0*k_1, k_1))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_18(x, k_0, k_1) + F_24(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_7(x))
Eq(F_13(x, k_0, k_1), (-k_0*F_14(x, k_0) + k_1*F_14(x, k_1))/(-k_0 + k_1))
Eq(F_14(x, k_0), F_15(x, k_0) + F_3(x))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_0(x)*F_14(x, k_0)*F_17(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0, k_1), F_17(x, k_0)*F_19(x, k_0, k_1))
Eq(F_19(x, k_0, k_1), (-k_0*F_20(x, k_0, 1) + k_1*F_20(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1), F_1(x) + F_21(x, k_0, k_1) + F_22(x, k_0, k_1) + F_23(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_12(x, k_0, k_0*k_1))
Eq(F_22(x, k_0, k_1), F_18(x, k_0, k_0*k_1))
Eq(F_23(x, k_0, k_1), F_17(x, k_1)*F_20(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), F_17(x, k_1)*F_25(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), (-k_0*F_10(x, k_0/k_1, k_1) + k_1*F_10(x, 1, k_1))/(-k_0 + k_1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_and_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "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, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "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, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "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, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 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, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 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