02143_02413_02431_04213_04231_20143_20413_20431

Counting sequence:
1, 1, 2, 6, 24, 112, 562, 2931, 15690, 85753, 476968, 2692904, 15398650, 89014193, 519366248, 3054715077, 18092383108, 107814079392, 645952458506, 3888772631544, 23512210755034, 142711110962299, 869253312772618, 5311553879372443, 32550957168642214, 200017510844811693, 1232088802805538738, 7606834873896719932, 47063175955743984188, 291748588176606541158, 1811875252278745495856, 11271645645324152579665, 70232547752941594908210, 438266790941719546813601, 2738726236266182963149756, 17136925413556248679172198, 107364021206345531724655560, 673435909308780542002352532, 4228807212068524129497185086, 26582649005537498530969743283, 167268423363699925967831307720, 1053521337589247756115548468034, 6641501639762854156095291982550, 41904836072724070653081112017124, 264618105980613977329088038340022, 1672308241430645329685280060744863, 10576436235083201491469773933252352, 66938273002451445196852267119200061, 423944049050141065108496867598926902, 2686761202973471338356701930602349633, 17038228115720478095831352973454213614, 108114431765806361146928988602517862730, 686430357088535769975369753118412739546, 4360669225973810499614006706944838847663, 27716889434791642054866852070907910628720, 176263282047732572475191972357394151878006, 1121494227839588880571900438575959302712916, 7139080939582984167309578238441507492765558, 45466371333089030290679433225857534094419596, 289690358038950636798506504343747152581250376, 1846574901735189328385401305398156817464773864, 11775589911890668944833377528753584568246983140, 75123410575465971223236211622163301063763060000, 479445349695009409519495423920302250644884325721, 3061037826480216368905143562746147930832397468180, 19550545894856286723364872664846199504135470736736, 124912171665540001527782620007597597721801316773226, 798365209798761832412425280645856294193852164299024, 5104402680757531102093703608355970048890661043892962, 32646034557120263597700425347986625512345941945715227, 208859395691520552960799603106401600462578353307373974, 1336631638569009955240941104993118324389663067940056359, 8556572342574295828302485283038851905784413230100842638, 54791687223392276598101571526248806173703746779067734915, 350956116298251172838733282524474053349758367123128854688, 2248593375711540236316722501284309773203490743889275739104, 14410724549217141422297413277746565033526376684316795966630, 92379247492783572880686899180987163111214785211333137426039, 592343722205531079652200787933492601633117398896434153651352, 3799103218496456852254559044024999028442225088866422995931873, 24372136590107801389265665070744597204910940114779868797626758, 156389898144874378285050718862355161726643538112361596655538223, 1003746043079219446525397493791317010940992942621071385171319408, 6443719349932031215113280843605968290135738826357597030310847406, 41375634014008400719277237462387629947160131017810997441609009568, 265733138739857583523055427344952862045628676841623409761183837444, 1707016032066818374039439098780181946305544912689377252409190080306, 10967766656329651788440696568031495528361129650902239769896978755465, 70483179759615631562959515768482549051385792419849531590749159246386, 453040985427526475985186885119940945072288623030577860497285469606031, 2912542803860326982664284580993741222703827465053224869530496442162830, 18727858615094551264574086629064374088322308321554120460443906373768644, 120443435087631906149286492448454002320746196662210019910965032436865692, 774739380425677145764825783700190669817149426469818600547541163478697574, 4984297485727151650698504184031617903413828107984858598980717212800625376, 32072033187871931971031576751979138880987479754101462255736035653079299649, 206405699454652714975484838581998881374315470245236998190284890374055650574, 1328580953757780627725326134008143713063075480120892676539682318251931798605, 8553109646033805744950025786801360997971555127732491505480767757185789850446, 55071679061688808185293385569659813720732372818025329841748698752255909404494, 354649605101969472072734257778619994820346190801405727919902085144699609367406

Implicit equation for the generating function in Maple syntax:
(4*x-1)*x*F(x)^6+(-16*x^2-2*x+1)*F(x)^5+(16*x^2+26*x-3)*F(x)^4+(-48*x-5)*F(x)^3+(24*x+25)*F(x)^2-27*F(x)+9 = 0

Implicit equation for the generating function in latex syntax:
\left(4 x -1\right) x F \! \left(x \right)^{6}+\left(-16 x^{2}-2 x +1\right) F \! \left(x \right)^{5}+\left(16 x^{2}+26 x -3\right) F \! \left(x \right)^{4}+\left(-48 x -5\right) F \! \left(x \right)^{3}+\left(24 x +25\right) F \! \left(x \right)^{2}-27 F \! \left(x \right)+9 = 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) = 2931
a(8) = 15690
a(9) = 85753
a(10) = 476968
a(11) = 2692904
a(12) = 15398650
a(13) = 89014193
a(14) = 519366248
a(15) = 3054715077
a(16) = 18092383108
a(17) = 107814079392
a(18) = 645952458506
a(19) = 3888772631544
a(20) = 23512210755034
a(21) = 142711110962299
a(22) = 869253312772618
a(23) = 5311553879372443
a(24) = 32550957168642214
a(25) = 200017510844811693
a(26) = 1232088802805538738
a(27) = 7606834873896719932
a(28) = 47063175955743984188
a(29) = 291748588176606541158
a(30) = 1811875252278745495856
a(n+31) = 24046319299461120/12131*(2*n+3)*(n+2)*(n+1)*(29731*n^2+152613*n+197700)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+1)-25048249270272/12131*(n+2)*(245617983*n^4+3015005864*n^3+13862355557*n^2+28254155316*n+21510584640)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+2)-1/1552768000*(582048882082744*n^4+65572088971265424*n^3+2757191584395862205*n^2+51313295333754781257*n+356797097475552592182)/(n+30)/(n+29)/(n+32)/(n+31)*a(n+27)+1/38819200*(1831118728090*n^3+150062500811607*n^2+4097910052131881*n+37290005274048714)/(n+30)/(n+32)/(n+31)*a(n+28)-1/19409600*(49836647801*n^2+2742764145823*n+37741815985512)/(n+32)/(n+31)*a(n+29)-5771116631870668800/1733*n*(2*n+3)*(2*n+1)*(n+2)*(n+1)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n)+3/485240*(12309991*n+343302762)/(n+32)*a(n+30)+1/4852400000*(754247901906419054347613*n^5+70587046077894686264553120*n^4+2642103739018935803971454525*n^3+49443529417029329299231644885*n^2+462609403017216405176197221917*n+1731272118193106292671139737790)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+19)-1/3881920000*(103620917227196614344073*n^5+10163891638838734388798474*n^4+398679520516378816796541494*n^3+7817308606264556793546655798*n^2+76624567664124226713153139851*n+300368346752959759625655370446)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+20)+1/7763840000*(30320472556834093590629*n^5+3108628569364730737700120*n^4+127432934278034486649042154*n^3+2610893226339518398107687727*n^2+26735944683417111094910116638*n+109470009106284226168353262488)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+21)-1/15527680000*(7431442793944725456023*n^5+794211367367501702654738*n^4+33930551719692965725531141*n^3+724347632670704134594676458*n^2+7726867122771289236543665472*n+32949480455463356099550289752)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+22)+1/31055360000*(1485422901254642746513*n^5+164972150191051379623516*n^4+7322155742382199014773499*n^3+162343773472387509093431468*n^2+1798001147615648690587142204*n+7957558945846738047355428000)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+23)-1/15527680000*(57686303184665061819*n^5+6629317627502869425188*n^4+304308552719489172046341*n^3+6974111892703138293657028*n^2+79792029661747033561497096*n+364567551107274100493780400)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+24)+3/31055360000*(2073574254782714349*n^5+244243024274772780024*n^4+11475478456513729442745*n^3+268759134843397196154002*n^2+3136659495251729791229952*n+14588696197463574550376320)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+25)-1/7763840000*(34594201652788176*n^5+3897347598423273217*n^4+172062607359326354207*n^3+3694072015268268110072*n^2+38103626659042879586116*n+147706398512481747246960)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+26)-16/37909375*(302271453752238665505889*n^5+21318384897896650271914030*n^4+601734343017711464554305870*n^3+8497212175011809279598168245*n^2+60032389325312885084400999686*n+169760661425372374325270936535)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+14)+4/7581875*(82206705529424544488412*n^5+6181261648260323995695104*n^4+185987945805716541369184944*n^3+2799351310797833739496853161*n^2+21077110095694146912477807519*n+63511267667607892954723503141)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+15)-3/37909375*(163865910772739526792856*n^5+13082186362475631923067240*n^4+417883126774076935876590380*n^3+6676336163247255721825745955*n^2+53351397228526361022995934469*n+170601277467845813188371121165)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+16)+1/303275000*(1031792380605269851936701*n^5+87136664087644880595789380*n^4+2943997072946191794453347245*n^3+49742350122059412838445850520*n^2+420321821656325679381535023614*n+1421045696701070689991615754990)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+17)-1/242620000*(189271344348479921812495*n^5+16852280921012119587380218*n^4+600211817419516323033119126*n^3+10689203102126549360708869775*n^2+95190524652962517046802834562*n+339118988679000956343030599106)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+18)+24576/37909375*(6215534204524538743999*n^5+292349202911276382477740*n^4+5506746199162866169756355*n^3+51924707119375239835729060*n^2+245097446400200432845645746*n+463311533260691901545666760)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+9)-6144/7581875*(3258891576657996993409*n^5+168623017896235826726998*n^4+3493673675960023118287214*n^3+36231683603489053341330053*n^2+188080024547162094820069686*n+390964452567407356966590456)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+10)+1536/37909375*(37197314893147533118471*n^5+2099759144151741547491760*n^4+47455941502919607345810015*n^3+536785194335902456706652815*n^2+3038863162669705616053042199*n+6888434473642515765576476880)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+11)-128/7581875*(44598202411812121403345*n^5+2727257059029128584261226*n^4+66763831471309189643424250*n^3+817881215716812434270270482*n^2+5014037199311991222239893707*n+12306508320187023110601644268)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+12)+64/37909375*(195697684894799856877214*n^5+12885879941160694729723300*n^4+339619086178799429180369415*n^3+4478655761441657753056887755*n^2+29552672240140927086369605056*n+78062605640760941432672328645)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+13)+452984832/1516375*(15081597096842221*n^5+426205613818745660*n^4+4822808178398459645*n^3+27309110730549610330*n^2+77363734805567987424*n+87693322384001985120)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+5)-37748736/7581875*(1147201747529839911*n^5+37790669318240309510*n^4+498590576716976842020*n^3+3292919668178114679535*n^2+10885222280105246099724*n+14405712166869868946880)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+6)+786432/37909375*(289083820321920588221*n^5+10878920513263202712440*n^4+163976406928881024367645*n^3+1237371884981580536509990*n^2+4674256272205046568010764*n+7070818524721208324412480)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+7)-196608/37909375*(1024673133031818455389*n^5+43375422632398155634290*n^4+735382963546424009295820*n^3+6241673276813163587555505*n^2+26521273425283465301096686*n+45129913425906071175016920)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+8)+2087354105856/12131*(8213252877*n^5+155450189108*n^4+1175156838675*n^3+4432149941500*n^2+8333403760788*n+6244445225952)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+3)-86973087744/60655*(1998626305201*n^5+47144168570257*n^4+444972277174067*n^3+2099833463101091*n^2+4952242152500064*n+4667539713463620)/(n+30)/(n+29)/(n+28)/(n+32)/(n+31)*a(n+4), n >= 31

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) = 2931
a \! \left(8\right) = 15690
a \! \left(9\right) = 85753
a \! \left(10\right) = 476968
a \! \left(11\right) = 2692904
a \! \left(12\right) = 15398650
a \! \left(13\right) = 89014193
a \! \left(14\right) = 519366248
a \! \left(15\right) = 3054715077
a \! \left(16\right) = 18092383108
a \! \left(17\right) = 107814079392
a \! \left(18\right) = 645952458506
a \! \left(19\right) = 3888772631544
a \! \left(20\right) = 23512210755034
a \! \left(21\right) = 142711110962299
a \! \left(22\right) = 869253312772618
a \! \left(23\right) = 5311553879372443
a \! \left(24\right) = 32550957168642214
a \! \left(25\right) = 200017510844811693
a \! \left(26\right) = 1232088802805538738
a \! \left(27\right) = 7606834873896719932
a \! \left(28\right) = 47063175955743984188
a \! \left(29\right) = 291748588176606541158
a \! \left(30\right) = 1811875252278745495856
a \! \left(n +31\right) = \frac{24046319299461120 \left(2 n +3\right) \left(n +2\right) \left(n +1\right) \left(29731 n^{2}+152613 n +197700\right) a \! \left(n +1\right)}{12131 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{25048249270272 \left(n +2\right) \left(245617983 n^{4}+3015005864 n^{3}+13862355557 n^{2}+28254155316 n +21510584640\right) a \! \left(n +2\right)}{12131 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{\left(582048882082744 n^{4}+65572088971265424 n^{3}+2757191584395862205 n^{2}+51313295333754781257 n +356797097475552592182\right) a \! \left(n +27\right)}{1552768000 \left(n +30\right) \left(n +29\right) \left(n +32\right) \left(n +31\right)}+\frac{\left(1831118728090 n^{3}+150062500811607 n^{2}+4097910052131881 n +37290005274048714\right) a \! \left(n +28\right)}{38819200 \left(n +30\right) \left(n +32\right) \left(n +31\right)}-\frac{\left(49836647801 n^{2}+2742764145823 n +37741815985512\right) a \! \left(n +29\right)}{19409600 \left(n +32\right) \left(n +31\right)}-\frac{5771116631870668800 n \left(2 n +3\right) \left(2 n +1\right) \left(n +2\right) \left(n +1\right) a \! \left(n \right)}{1733 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}+\frac{3 \left(12309991 n +343302762\right) a \! \left(n +30\right)}{485240 \left(n +32\right)}+\frac{\left(754247901906419054347613 n^{5}+70587046077894686264553120 n^{4}+2642103739018935803971454525 n^{3}+49443529417029329299231644885 n^{2}+462609403017216405176197221917 n +1731272118193106292671139737790\right) a \! \left(n +19\right)}{4852400000 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{\left(103620917227196614344073 n^{5}+10163891638838734388798474 n^{4}+398679520516378816796541494 n^{3}+7817308606264556793546655798 n^{2}+76624567664124226713153139851 n +300368346752959759625655370446\right) a \! \left(n +20\right)}{3881920000 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}+\frac{\left(30320472556834093590629 n^{5}+3108628569364730737700120 n^{4}+127432934278034486649042154 n^{3}+2610893226339518398107687727 n^{2}+26735944683417111094910116638 n +109470009106284226168353262488\right) a \! \left(n +21\right)}{7763840000 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{\left(7431442793944725456023 n^{5}+794211367367501702654738 n^{4}+33930551719692965725531141 n^{3}+724347632670704134594676458 n^{2}+7726867122771289236543665472 n +32949480455463356099550289752\right) a \! \left(n +22\right)}{15527680000 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}+\frac{\left(1485422901254642746513 n^{5}+164972150191051379623516 n^{4}+7322155742382199014773499 n^{3}+162343773472387509093431468 n^{2}+1798001147615648690587142204 n +7957558945846738047355428000\right) a \! \left(n +23\right)}{31055360000 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{\left(57686303184665061819 n^{5}+6629317627502869425188 n^{4}+304308552719489172046341 n^{3}+6974111892703138293657028 n^{2}+79792029661747033561497096 n +364567551107274100493780400\right) a \! \left(n +24\right)}{15527680000 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}+\frac{3 \left(2073574254782714349 n^{5}+244243024274772780024 n^{4}+11475478456513729442745 n^{3}+268759134843397196154002 n^{2}+3136659495251729791229952 n +14588696197463574550376320\right) a \! \left(n +25\right)}{31055360000 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{\left(34594201652788176 n^{5}+3897347598423273217 n^{4}+172062607359326354207 n^{3}+3694072015268268110072 n^{2}+38103626659042879586116 n +147706398512481747246960\right) a \! \left(n +26\right)}{7763840000 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{16 \left(302271453752238665505889 n^{5}+21318384897896650271914030 n^{4}+601734343017711464554305870 n^{3}+8497212175011809279598168245 n^{2}+60032389325312885084400999686 n +169760661425372374325270936535\right) a \! \left(n +14\right)}{37909375 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}+\frac{4 \left(82206705529424544488412 n^{5}+6181261648260323995695104 n^{4}+185987945805716541369184944 n^{3}+2799351310797833739496853161 n^{2}+21077110095694146912477807519 n +63511267667607892954723503141\right) a \! \left(n +15\right)}{7581875 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{3 \left(163865910772739526792856 n^{5}+13082186362475631923067240 n^{4}+417883126774076935876590380 n^{3}+6676336163247255721825745955 n^{2}+53351397228526361022995934469 n +170601277467845813188371121165\right) a \! \left(n +16\right)}{37909375 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}+\frac{\left(1031792380605269851936701 n^{5}+87136664087644880595789380 n^{4}+2943997072946191794453347245 n^{3}+49742350122059412838445850520 n^{2}+420321821656325679381535023614 n +1421045696701070689991615754990\right) a \! \left(n +17\right)}{303275000 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{\left(189271344348479921812495 n^{5}+16852280921012119587380218 n^{4}+600211817419516323033119126 n^{3}+10689203102126549360708869775 n^{2}+95190524652962517046802834562 n +339118988679000956343030599106\right) a \! \left(n +18\right)}{242620000 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}+\frac{24576 \left(6215534204524538743999 n^{5}+292349202911276382477740 n^{4}+5506746199162866169756355 n^{3}+51924707119375239835729060 n^{2}+245097446400200432845645746 n +463311533260691901545666760\right) a \! \left(n +9\right)}{37909375 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{6144 \left(3258891576657996993409 n^{5}+168623017896235826726998 n^{4}+3493673675960023118287214 n^{3}+36231683603489053341330053 n^{2}+188080024547162094820069686 n +390964452567407356966590456\right) a \! \left(n +10\right)}{7581875 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}+\frac{1536 \left(37197314893147533118471 n^{5}+2099759144151741547491760 n^{4}+47455941502919607345810015 n^{3}+536785194335902456706652815 n^{2}+3038863162669705616053042199 n +6888434473642515765576476880\right) a \! \left(n +11\right)}{37909375 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{128 \left(44598202411812121403345 n^{5}+2727257059029128584261226 n^{4}+66763831471309189643424250 n^{3}+817881215716812434270270482 n^{2}+5014037199311991222239893707 n +12306508320187023110601644268\right) a \! \left(n +12\right)}{7581875 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}+\frac{64 \left(195697684894799856877214 n^{5}+12885879941160694729723300 n^{4}+339619086178799429180369415 n^{3}+4478655761441657753056887755 n^{2}+29552672240140927086369605056 n +78062605640760941432672328645\right) a \! \left(n +13\right)}{37909375 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}+\frac{452984832 \left(15081597096842221 n^{5}+426205613818745660 n^{4}+4822808178398459645 n^{3}+27309110730549610330 n^{2}+77363734805567987424 n +87693322384001985120\right) a \! \left(n +5\right)}{1516375 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{37748736 \left(1147201747529839911 n^{5}+37790669318240309510 n^{4}+498590576716976842020 n^{3}+3292919668178114679535 n^{2}+10885222280105246099724 n +14405712166869868946880\right) a \! \left(n +6\right)}{7581875 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}+\frac{786432 \left(289083820321920588221 n^{5}+10878920513263202712440 n^{4}+163976406928881024367645 n^{3}+1237371884981580536509990 n^{2}+4674256272205046568010764 n +7070818524721208324412480\right) a \! \left(n +7\right)}{37909375 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{196608 \left(1024673133031818455389 n^{5}+43375422632398155634290 n^{4}+735382963546424009295820 n^{3}+6241673276813163587555505 n^{2}+26521273425283465301096686 n +45129913425906071175016920\right) a \! \left(n +8\right)}{37909375 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}+\frac{2087354105856 \left(8213252877 n^{5}+155450189108 n^{4}+1175156838675 n^{3}+4432149941500 n^{2}+8333403760788 n +6244445225952\right) a \! \left(n +3\right)}{12131 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}-\frac{86973087744 \left(1998626305201 n^{5}+47144168570257 n^{4}+444972277174067 n^{3}+2099833463101091 n^{2}+4952242152500064 n +4667539713463620\right) a \! \left(n +4\right)}{60655 \left(n +30\right) \left(n +29\right) \left(n +28\right) \left(n +32\right) \left(n +31\right)}, \quad n \geq 31

Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24165/
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[23,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[23,x]*F[7,x]
F[7,x] = F[71,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[23,x]
F[11,x] = 1/F[23,x]*F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]*F[4,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[195,x]*F[23,x]
F[17,x] = F[18,x]+F[71,x]
F[18,x] = F[19,x]+F[25,x]
F[19,x] = F[20,x]+F[24,x]
F[20,x] = F[21,x]+F[4,x]
F[21,x] = F[22,x]
F[22,x] = F[17,x]*F[23,x]
F[23,x] = x
F[24,x] = F[21,x]
F[25,x] = F[26,x]
F[26,x] = F[23,x]*F[27,x]
F[27,x] = 1/F[23,x]/F[34,x]*F[28,x]
F[28,x] = F[29,x]
F[29,x] = -F[33,x]+F[30,x]
F[30,x] = 1/F[23,x]*F[31,x]
F[31,x] = F[32,x]
F[32,x] = -F[4,x]+F[8,x]
F[33,x] = F[0,x]*F[7,x]
F[34,x] = F[0,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[23,x]*F[37,x]
F[37,x] = 1/F[182,x]/F[23,x]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = -F[48,x]+F[40,x]
F[40,x] = 1/F[23,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[23,x]*F[43,x]
F[43,x] = 1/F[23,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = -F[0,x]+F[46,x]
F[46,x] = 1/F[23,x]*F[47,x]
F[47,x] = F[2,x]
F[48,x] = -F[49,x]+F[43,x]
F[49,x] = F[104,x]+F[50,x]
F[50,x] = -F[46,x]+F[51,x]
F[51,x] = F[52,x]+F[99,x]
F[52,x] = -F[94,x]+F[53,x]
F[53,x] = -F[56,x]+F[54,x]
F[54,x] = 1/F[23,x]*F[55,x]
F[55,x] = F[45,x]
F[56,x] = F[57,x]+F[61,x]
F[57,x] = F[0,x]*F[58,x]
F[58,x] = -F[0,x]+F[59,x]
F[59,x] = 1/F[23,x]*F[60,x]
F[60,x] = F[2,x]
F[61,x] = F[62,x]
F[62,x] = F[23,x]*F[63,x]*F[81,x]
F[63,x] = F[64,x]+F[76,x]
F[64,x] = F[65,x]*F[73,x]
F[65,x] = F[0,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[23,x]*F[68,x]
F[68,x] = F[69,x]+F[71,x]
F[69,x] = F[65,x]+F[70,x]
F[70,x] = F[66,x]
F[71,x] = F[72,x]
F[72,x] = F[17,x]*F[23,x]
F[73,x] = F[74,x]
F[74,x] = F[23,x]*F[75,x]
F[75,x] = F[1,x]+F[73,x]
F[76,x] = F[77,x]
F[77,x] = F[23,x]*F[75,x]*F[78,x]
F[78,x] = 1/F[23,x]/F[34,x]*F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[15,x]+F[21,x]
F[81,x] = F[37,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[23,x]*F[81,x]*F[84,x]
F[84,x] = F[75,x]+F[85,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[87,x]
F[87,x] = F[23,x]*F[88,x]
F[88,x] = F[1,x]+F[86,x]
F[89,x] = F[90,x]+F[91,x]+F[93,x]
F[90,x] = 0
F[91,x] = F[23,x]*F[92,x]
F[92,x] = F[73,x]+F[89,x]
F[93,x] = F[23,x]*F[85,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[0,x]*F[2,x]
F[96,x] = F[97,x]
F[97,x] = F[23,x]*F[81,x]*F[98,x]
F[98,x] = F[2,x]+F[66,x]
F[99,x] = F[100,x]+F[45,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[23,x]*F[88,x]
F[102,x] = F[103,x]
F[103,x] = F[23,x]*F[81,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[23,x]*F[81,x]
F[106,x] = F[107,x]+F[133,x]
F[107,x] = F[108,x]+F[110,x]
F[108,x] = F[109,x]
F[109,x] = F[23,x]*F[84,x]
F[110,x] = F[111,x]+F[73,x]
F[111,x] = F[112,x]+F[114,x]+F[90,x]
F[112,x] = F[113,x]*F[23,x]
F[113,x] = F[108,x]+F[111,x]
F[114,x] = F[115,x]*F[23,x]
F[115,x] = F[116,x]+F[121,x]
F[116,x] = F[117,x]+F[73,x]
F[117,x] = F[118,x]+F[120,x]+F[90,x]
F[118,x] = F[119,x]*F[23,x]
F[119,x] = F[117,x]+F[73,x]
F[120,x] = F[116,x]*F[23,x]
F[121,x] = F[122,x]+F[127,x]
F[122,x] = F[123,x]+F[125,x]+F[90,x]
F[123,x] = F[124,x]*F[23,x]
F[124,x] = F[122,x]+F[86,x]
F[125,x] = F[126,x]*F[23,x]
F[126,x] = F[122,x]+F[73,x]
F[127,x] = F[128,x]+F[130,x]+F[132,x]+F[90,x]
F[128,x] = F[129,x]*F[23,x]
F[129,x] = F[127,x]+F[89,x]
F[130,x] = F[131,x]*F[23,x]
F[131,x] = F[117,x]+F[127,x]
F[132,x] = F[121,x]*F[23,x]
F[133,x] = F[134,x]+F[151,x]
F[134,x] = F[135,x]+F[137,x]+F[90,x]
F[135,x] = F[136,x]*F[23,x]
F[136,x] = F[108,x]+F[134,x]
F[137,x] = F[138,x]*F[23,x]
F[138,x] = F[139,x]+F[85,x]
F[139,x] = F[140,x]+F[145,x]
F[140,x] = F[141,x]+F[143,x]+F[90,x]
F[141,x] = F[142,x]*F[23,x]
F[142,x] = F[140,x]+F[86,x]
F[143,x] = F[144,x]*F[23,x]
F[144,x] = F[140,x]+F[86,x]
F[145,x] = F[146,x]+F[148,x]+F[150,x]+F[90,x]
F[146,x] = F[147,x]*F[23,x]
F[147,x] = F[145,x]+F[89,x]
F[148,x] = F[149,x]*F[23,x]
F[149,x] = F[145,x]+F[89,x]
F[150,x] = F[139,x]*F[23,x]
F[151,x] = F[152,x]+F[89,x]
F[152,x] = F[153,x]+F[155,x]+F[157,x]+F[90,x]
F[153,x] = F[154,x]*F[23,x]
F[154,x] = F[111,x]+F[152,x]
F[155,x] = F[156,x]*F[23,x]
F[156,x] = F[134,x]+F[152,x]
F[157,x] = F[158,x]*F[23,x]
F[158,x] = F[159,x]+F[166,x]
F[159,x] = F[160,x]+F[89,x]
F[160,x] = F[161,x]+F[163,x]+F[165,x]+F[90,x]
F[161,x] = F[162,x]*F[23,x]
F[162,x] = F[117,x]+F[160,x]
F[163,x] = F[164,x]*F[23,x]
F[164,x] = F[160,x]+F[89,x]
F[165,x] = F[159,x]*F[23,x]
F[166,x] = F[167,x]+F[174,x]
F[167,x] = F[168,x]+F[170,x]+F[172,x]+F[90,x]
F[168,x] = F[169,x]*F[23,x]
F[169,x] = F[122,x]+F[167,x]
F[170,x] = F[171,x]*F[23,x]
F[171,x] = F[140,x]+F[167,x]
F[172,x] = F[173,x]*F[23,x]
F[173,x] = F[167,x]+F[89,x]
F[174,x] = F[175,x]+F[177,x]+F[179,x]+F[181,x]+F[90,x]
F[175,x] = F[176,x]*F[23,x]
F[176,x] = F[127,x]+F[174,x]
F[177,x] = F[178,x]*F[23,x]
F[178,x] = F[145,x]+F[174,x]
F[179,x] = F[180,x]*F[23,x]
F[180,x] = F[160,x]+F[174,x]
F[181,x] = F[166,x]*F[23,x]
F[182,x] = F[183,x]+F[189,x]
F[183,x] = F[184,x]+F[187,x]
F[184,x] = F[185,x]+F[186,x]
F[185,x] = F[1,x]+F[108,x]
F[186,x] = F[108,x]
F[187,x] = F[110,x]+F[188,x]
F[188,x] = F[111,x]
F[189,x] = F[190,x]+F[193,x]
F[190,x] = F[191,x]+F[192,x]
F[191,x] = F[134,x]+F[86,x]
F[192,x] = F[134,x]
F[193,x] = F[151,x]+F[194,x]
F[194,x] = F[152,x]
F[195,x] = F[2,x]+F[35,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_{23}\! \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_{23}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{71}\! \left(x \right)+F_{8}\! \left(x \right)
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_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{195}\! \left(x \right) F_{23}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{71}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{25}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{24}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{17}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{21}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{23}\! \left(x \right) F_{34}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = -F_{33}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{8}\! \left(x \right)
F_{33}\! \left(x \right) = F_{0}\! \left(x \right) F_{7}\! \left(x \right)
F_{34}\! \left(x \right) = F_{0}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{23}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{182}\! \left(x \right) F_{23}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{23}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{2}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{49}\! \left(x \right)+F_{43}\! \left(x \right)
F_{49}\! \left(x \right) = F_{104}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{99}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{94}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{56}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{45}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{57}\! \left(x \right) = F_{0}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{2}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{23}\! \left(x \right) F_{63}\! \left(x \right) F_{81}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{76}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right) F_{73}\! \left(x \right)
F_{65}\! \left(x \right) = F_{0}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{23}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{65}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{66}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{17}\! \left(x \right) F_{23}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{23}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{23}\! \left(x \right) F_{75}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{23}\! \left(x \right) F_{34}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{15}\! \left(x \right)+F_{21}\! \left(x \right)
F_{81}\! \left(x \right) = F_{37}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{23}\! \left(x \right) F_{81}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{75}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{23}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{1}\! \left(x \right)+F_{86}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)+F_{93}\! \left(x \right)
F_{90}\! \left(x \right) = 0
F_{91}\! \left(x \right) = F_{23}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{73}\! \left(x \right)+F_{89}\! \left(x \right)
F_{93}\! \left(x \right) = F_{23}\! \left(x \right) F_{85}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{23}\! \left(x \right) F_{81}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{2}\! \left(x \right)+F_{66}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{45}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{23}\! \left(x \right) F_{88}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{23}\! \left(x \right) F_{81}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{23}\! \left(x \right) F_{81}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{133}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{110}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{23}\! \left(x \right) F_{84}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{73}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{114}\! \left(x \right)+F_{90}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{23}\! \left(x \right)
F_{113}\! \left(x \right) = F_{108}\! \left(x \right)+F_{111}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{23}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{121}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{73}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{120}\! \left(x \right)+F_{90}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{23}\! \left(x \right)
F_{119}\! \left(x \right) = F_{117}\! \left(x \right)+F_{73}\! \left(x \right)
F_{120}\! \left(x \right) = F_{116}\! \left(x \right) F_{23}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{127}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{125}\! \left(x \right)+F_{90}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{23}\! \left(x \right)
F_{124}\! \left(x \right) = F_{122}\! \left(x \right)+F_{86}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{23}\! \left(x \right)
F_{126}\! \left(x \right) = F_{122}\! \left(x \right)+F_{73}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{130}\! \left(x \right)+F_{132}\! \left(x \right)+F_{90}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{23}\! \left(x \right)
F_{129}\! \left(x \right) = F_{127}\! \left(x \right)+F_{89}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{23}\! \left(x \right)
F_{131}\! \left(x \right) = F_{117}\! \left(x \right)+F_{127}\! \left(x \right)
F_{132}\! \left(x \right) = F_{121}\! \left(x \right) F_{23}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{151}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{137}\! \left(x \right)+F_{90}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{23}\! \left(x \right)
F_{136}\! \left(x \right) = F_{108}\! \left(x \right)+F_{134}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{23}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{85}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{145}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{143}\! \left(x \right)+F_{90}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{23}\! \left(x \right)
F_{142}\! \left(x \right) = F_{140}\! \left(x \right)+F_{86}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{23}\! \left(x \right)
F_{144}\! \left(x \right) = F_{140}\! \left(x \right)+F_{86}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{148}\! \left(x \right)+F_{150}\! \left(x \right)+F_{90}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right) F_{23}\! \left(x \right)
F_{147}\! \left(x \right) = F_{145}\! \left(x \right)+F_{89}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{23}\! \left(x \right)
F_{149}\! \left(x \right) = F_{145}\! \left(x \right)+F_{89}\! \left(x \right)
F_{150}\! \left(x \right) = F_{139}\! \left(x \right) F_{23}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{89}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{155}\! \left(x \right)+F_{157}\! \left(x \right)+F_{90}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{23}\! \left(x \right)
F_{154}\! \left(x \right) = F_{111}\! \left(x \right)+F_{152}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right) F_{23}\! \left(x \right)
F_{156}\! \left(x \right) = F_{134}\! \left(x \right)+F_{152}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{23}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{166}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{89}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{163}\! \left(x \right)+F_{165}\! \left(x \right)+F_{90}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right) F_{23}\! \left(x \right)
F_{162}\! \left(x \right) = F_{117}\! \left(x \right)+F_{160}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right) F_{23}\! \left(x \right)
F_{164}\! \left(x \right) = F_{160}\! \left(x \right)+F_{89}\! \left(x \right)
F_{165}\! \left(x \right) = F_{159}\! \left(x \right) F_{23}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{174}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{170}\! \left(x \right)+F_{172}\! \left(x \right)+F_{90}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right) F_{23}\! \left(x \right)
F_{169}\! \left(x \right) = F_{122}\! \left(x \right)+F_{167}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{23}\! \left(x \right)
F_{171}\! \left(x \right) = F_{140}\! \left(x \right)+F_{167}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right) F_{23}\! \left(x \right)
F_{173}\! \left(x \right) = F_{167}\! \left(x \right)+F_{89}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{177}\! \left(x \right)+F_{179}\! \left(x \right)+F_{181}\! \left(x \right)+F_{90}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right) F_{23}\! \left(x \right)
F_{176}\! \left(x \right) = F_{127}\! \left(x \right)+F_{174}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right) F_{23}\! \left(x \right)
F_{178}\! \left(x \right) = F_{145}\! \left(x \right)+F_{174}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right) F_{23}\! \left(x \right)
F_{180}\! \left(x \right) = F_{160}\! \left(x \right)+F_{174}\! \left(x \right)
F_{181}\! \left(x \right) = F_{166}\! \left(x \right) F_{23}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)+F_{189}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{187}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{186}\! \left(x \right)
F_{185}\! \left(x \right) = F_{1}\! \left(x \right)+F_{108}\! \left(x \right)
F_{186}\! \left(x \right) = F_{108}\! \left(x \right)
F_{187}\! \left(x \right) = F_{110}\! \left(x \right)+F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{111}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{193}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{192}\! \left(x \right)
F_{191}\! \left(x \right) = F_{134}\! \left(x \right)+F_{86}\! \left(x \right)
F_{192}\! \left(x \right) = F_{134}\! \left(x \right)
F_{193}\! \left(x \right) = F_{151}\! \left(x \right)+F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{152}\! \left(x \right)
F_{195}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \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_23(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_23(x)*F_7(x))
Eq(F_7(x), F_71(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_23(x))
Eq(F_11(x), F_12(x)/F_23(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x)*F_4(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_195(x)*F_23(x))
Eq(F_17(x), F_18(x) + F_71(x))
Eq(F_18(x), F_19(x) + F_25(x))
Eq(F_19(x), F_20(x) + F_24(x))
Eq(F_20(x), F_21(x) + F_4(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_17(x)*F_23(x))
Eq(F_23(x), x)
Eq(F_24(x), F_21(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_23(x)*F_27(x))
Eq(F_27(x), F_28(x)/(F_23(x)*F_34(x)))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x) - F_33(x))
Eq(F_30(x), F_31(x)/F_23(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), -F_4(x) + F_8(x))
Eq(F_33(x), F_0(x)*F_7(x))
Eq(F_34(x), F_0(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_23(x)*F_37(x))
Eq(F_37(x), F_38(x)/(F_182(x)*F_23(x)))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_40(x) - F_48(x))
Eq(F_40(x), F_41(x)/F_23(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_23(x)*F_43(x))
Eq(F_43(x), F_44(x)/F_23(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), -F_0(x) + F_46(x))
Eq(F_46(x), F_47(x)/F_23(x))
Eq(F_47(x), F_2(x))
Eq(F_48(x), F_43(x) - F_49(x))
Eq(F_49(x), F_104(x) + F_50(x))
Eq(F_50(x), -F_46(x) + F_51(x))
Eq(F_51(x), F_52(x) + F_99(x))
Eq(F_52(x), F_53(x) - F_94(x))
Eq(F_53(x), F_54(x) - F_56(x))
Eq(F_54(x), F_55(x)/F_23(x))
Eq(F_55(x), F_45(x))
Eq(F_56(x), F_57(x) + F_61(x))
Eq(F_57(x), F_0(x)*F_58(x))
Eq(F_58(x), -F_0(x) + F_59(x))
Eq(F_59(x), F_60(x)/F_23(x))
Eq(F_60(x), F_2(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_23(x)*F_63(x)*F_81(x))
Eq(F_63(x), F_64(x) + F_76(x))
Eq(F_64(x), F_65(x)*F_73(x))
Eq(F_65(x), F_0(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_23(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_71(x))
Eq(F_69(x), F_65(x) + F_70(x))
Eq(F_70(x), F_66(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_17(x)*F_23(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_23(x)*F_75(x))
Eq(F_75(x), F_1(x) + F_73(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_23(x)*F_75(x)*F_78(x))
Eq(F_78(x), F_79(x)/(F_23(x)*F_34(x)))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_15(x) + F_21(x))
Eq(F_81(x), F_37(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_23(x)*F_81(x)*F_84(x))
Eq(F_84(x), F_75(x) + F_85(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_23(x)*F_88(x))
Eq(F_88(x), F_1(x) + F_86(x))
Eq(F_89(x), F_90(x) + F_91(x) + F_93(x))
Eq(F_90(x), 0)
Eq(F_91(x), F_23(x)*F_92(x))
Eq(F_92(x), F_73(x) + F_89(x))
Eq(F_93(x), F_23(x)*F_85(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_0(x)*F_2(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_23(x)*F_81(x)*F_98(x))
Eq(F_98(x), F_2(x) + F_66(x))
Eq(F_99(x), F_100(x) + F_45(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_23(x)*F_88(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_23(x)*F_81(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_23(x)*F_81(x))
Eq(F_106(x), F_107(x) + F_133(x))
Eq(F_107(x), F_108(x) + F_110(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_23(x)*F_84(x))
Eq(F_110(x), F_111(x) + F_73(x))
Eq(F_111(x), F_112(x) + F_114(x) + F_90(x))
Eq(F_112(x), F_113(x)*F_23(x))
Eq(F_113(x), F_108(x) + F_111(x))
Eq(F_114(x), F_115(x)*F_23(x))
Eq(F_115(x), F_116(x) + F_121(x))
Eq(F_116(x), F_117(x) + F_73(x))
Eq(F_117(x), F_118(x) + F_120(x) + F_90(x))
Eq(F_118(x), F_119(x)*F_23(x))
Eq(F_119(x), F_117(x) + F_73(x))
Eq(F_120(x), F_116(x)*F_23(x))
Eq(F_121(x), F_122(x) + F_127(x))
Eq(F_122(x), F_123(x) + F_125(x) + F_90(x))
Eq(F_123(x), F_124(x)*F_23(x))
Eq(F_124(x), F_122(x) + F_86(x))
Eq(F_125(x), F_126(x)*F_23(x))
Eq(F_126(x), F_122(x) + F_73(x))
Eq(F_127(x), F_128(x) + F_130(x) + F_132(x) + F_90(x))
Eq(F_128(x), F_129(x)*F_23(x))
Eq(F_129(x), F_127(x) + F_89(x))
Eq(F_130(x), F_131(x)*F_23(x))
Eq(F_131(x), F_117(x) + F_127(x))
Eq(F_132(x), F_121(x)*F_23(x))
Eq(F_133(x), F_134(x) + F_151(x))
Eq(F_134(x), F_135(x) + F_137(x) + F_90(x))
Eq(F_135(x), F_136(x)*F_23(x))
Eq(F_136(x), F_108(x) + F_134(x))
Eq(F_137(x), F_138(x)*F_23(x))
Eq(F_138(x), F_139(x) + F_85(x))
Eq(F_139(x), F_140(x) + F_145(x))
Eq(F_140(x), F_141(x) + F_143(x) + F_90(x))
Eq(F_141(x), F_142(x)*F_23(x))
Eq(F_142(x), F_140(x) + F_86(x))
Eq(F_143(x), F_144(x)*F_23(x))
Eq(F_144(x), F_140(x) + F_86(x))
Eq(F_145(x), F_146(x) + F_148(x) + F_150(x) + F_90(x))
Eq(F_146(x), F_147(x)*F_23(x))
Eq(F_147(x), F_145(x) + F_89(x))
Eq(F_148(x), F_149(x)*F_23(x))
Eq(F_149(x), F_145(x) + F_89(x))
Eq(F_150(x), F_139(x)*F_23(x))
Eq(F_151(x), F_152(x) + F_89(x))
Eq(F_152(x), F_153(x) + F_155(x) + F_157(x) + F_90(x))
Eq(F_153(x), F_154(x)*F_23(x))
Eq(F_154(x), F_111(x) + F_152(x))
Eq(F_155(x), F_156(x)*F_23(x))
Eq(F_156(x), F_134(x) + F_152(x))
Eq(F_157(x), F_158(x)*F_23(x))
Eq(F_158(x), F_159(x) + F_166(x))
Eq(F_159(x), F_160(x) + F_89(x))
Eq(F_160(x), F_161(x) + F_163(x) + F_165(x) + F_90(x))
Eq(F_161(x), F_162(x)*F_23(x))
Eq(F_162(x), F_117(x) + F_160(x))
Eq(F_163(x), F_164(x)*F_23(x))
Eq(F_164(x), F_160(x) + F_89(x))
Eq(F_165(x), F_159(x)*F_23(x))
Eq(F_166(x), F_167(x) + F_174(x))
Eq(F_167(x), F_168(x) + F_170(x) + F_172(x) + F_90(x))
Eq(F_168(x), F_169(x)*F_23(x))
Eq(F_169(x), F_122(x) + F_167(x))
Eq(F_170(x), F_171(x)*F_23(x))
Eq(F_171(x), F_140(x) + F_167(x))
Eq(F_172(x), F_173(x)*F_23(x))
Eq(F_173(x), F_167(x) + F_89(x))
Eq(F_174(x), F_175(x) + F_177(x) + F_179(x) + F_181(x) + F_90(x))
Eq(F_175(x), F_176(x)*F_23(x))
Eq(F_176(x), F_127(x) + F_174(x))
Eq(F_177(x), F_178(x)*F_23(x))
Eq(F_178(x), F_145(x) + F_174(x))
Eq(F_179(x), F_180(x)*F_23(x))
Eq(F_180(x), F_160(x) + F_174(x))
Eq(F_181(x), F_166(x)*F_23(x))
Eq(F_182(x), F_183(x) + F_189(x))
Eq(F_183(x), F_184(x) + F_187(x))
Eq(F_184(x), F_185(x) + F_186(x))
Eq(F_185(x), F_1(x) + F_108(x))
Eq(F_186(x), F_108(x))
Eq(F_187(x), F_110(x) + F_188(x))
Eq(F_188(x), F_111(x))
Eq(F_189(x), F_190(x) + F_193(x))
Eq(F_190(x), F_191(x) + F_192(x))
Eq(F_191(x), F_134(x) + F_86(x))
Eq(F_192(x), F_134(x))
Eq(F_193(x), F_151(x) + F_194(x))
Eq(F_194(x), F_152(x))
Eq(F_195(x), F_2(x) + F_35(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": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 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]]}], "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 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": [[1, 0], [1, 0], [1, 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": [[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], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 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], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 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], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "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], [0, 0], [0, 0], [0, 0], [1, 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]]}], "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": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 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": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 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": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 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], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 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], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 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], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 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], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", 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