02341_02413_02431_03241_03421_04213_04231_04321_20341_20413_20431
Counting sequence:
1, 1, 2, 6, 24, 109, 522, 2584, 13140, 68320, 361656, 1942474, 10558944, 57978138, 321105516, 1791691792, 10062353548, 56835384632, 322656494440, 1840046669608, 10536209903392, 60553103888697, 349170624013994, 2019577859467256, 11713686474429020, 68114364455915216, 397017273546018152, 2319150124966716780, 13574648521962000992, 79606267138546660308, 467659456450466989240, 2751859293082459366944, 16217791988926509393404, 95716170419447975867400, 565678560822714712392456, 3347425289926501708472536, 19832508450100511038360608, 117636297407802250730795940, 698514828036457641770242504, 4151988874849804129865656288, 24703615679269079342157399376, 147118683904735863659301940224, 876917594074195364449021322976, 5231369707764399022030581216714, 31233523955462315933054392985664, 186620734195551495582343197905794, 1115880140451830971446470400585788, 6676983486690824917259099134560848, 39979316443150789337359638470591220, 239535966601194257609565861735538024, 1436068407637904291608616806196574104, 8614656013186769364717731865367235704, 51706980151649126602176835601202985952, 310527025449230958009145728248560259518, 1865862890593960081320170055205446776940, 11217129527637161132225568533440383416208, 67467942656826750914269029105056082419688, 405993786021076214629159961211395789806112, 2444220301890015856288001213089115916522736, 14721551012178421770299775941089581983931960, 88705921110210971437607005809983841215370304, 534726060535252998459218082787776463591580456, 3224660262715941501013827998240083146705730800, 19453820777418521190509645786306410166434109504, 117405623746426537469714864355011666430918671580, 708811729159498590561125298462372661507460383016, 4280811327887415260291642259275384861443821034824, 25862462999810366320566863555749430930215224049016, 156299608962218530530802752131649868425164581526048, 944900147522654150500347016958835908433233486240764, 5714127691118263003039574492785812414906776373109048, 34565760608381394000860219400340886003217904985905440, 209156208778705638758609623688955806854902356688787440, 1265961030586241565056979465414613151688659340818540928, 7664634618265532753250186109656205028023183588724379808, 46417405808354171520964520003261423168306284268369842376, 281180654624080766874703787113517007442035637985892920448, 1703735498961753409705009264920844960771681178570757144648, 10325906360519067512090861354304558604826942733035488981232, 62598033593387810055389305813681427835560060639893918993216, 379574497419196355907243362920518896209975286953405714730160, 2302155283619324562065545544189160758900647564695856426115296, 13965965910538802404987376198949996503855341569780590983202976, 84742979215915923290614721054510015642195652835189629530347168, 514316624100378073893504419395071444010787959615430034496585856, 3122117609658182474447218788606479393697192835633201783342154409, 18956479019745363325246374791503531360486926579680041367729137962, 115120784335956305462551297340949365208965736212099474312060054904, 699254799837061852763121953989389589857497775646501210349725137596, 4248160264328895559332102276980762869664683777010333769173371578896, 25813576586604967567921767633241215603832053981098316709957724219304, 156882868208078515829329093179198784312450535224393951679941593239996, 953632761041622140745889564215180071275790523721855753646107146448224, 5797802510287653419739158699701826121009415945307686541948343095125732, 35254994587846863636894174668844582112339118975294420573600711141277336, 214413083349858945908204525445282625135226926686366605230315400502185120, 1304228763274946908243679577681716225505178890731577732388378059228469540, 7934629290994326417404472946816197137627919470085136431956563764031067128, 48280131425967103742650326356585502993603547082655545661033536847614399160, 293817584876485396127373902842491869624998236864850754093316057871376291752, 1788353254312117890490207131656735938492294538383976395516884869708284440800
Implicit equation for the generating function in Maple syntax:
2*x^2*F(x)^6-4*x^2*F(x)^5+x*(2*x+1)*F(x)^4-2*x*F(x)^3+2*x*F(x)^2-F(x)+1 = 0
Implicit equation for the generating function in latex syntax:
2 x^{2} F \! \left(x \right)^{6}-4 x^{2} F \! \left(x \right)^{5}+x \left(2 x +1\right) F \! \left(x \right)^{4}-2 x F \! \left(x \right)^{3}+2 x F \! \left(x \right)^{2}-F \! \left(x \right)+1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 109
a(6) = 522
a(7) = 2584
a(8) = 13140
a(9) = 68320
a(10) = 361656
a(11) = 1942474
a(12) = 10558944
a(13) = 57978138
a(14) = 321105516
a(15) = 1791691792
a(16) = 10062353548
a(17) = 56835384632
a(18) = 322656494440
a(19) = 1840046669608
a(n+20) = -66538438656/115*n*(2*n+5)*(2*n+3)*(2*n+1)*(n+2)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n)-25165824/575*(2*n+5)*(2*n+3)*(826051*n^3+5251606*n^2+10766816*n+6331346)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+1)-1048576/575*(2*n+5)*(419744543*n^4+4753917485*n^3+20140200060*n^2+37657506080*n+26055162252)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+2)-524288/5175*(56243430352*n^5+950757418235*n^4+6347953992500*n^3+20877992358460*n^2+33734532761073*n+21351583420020)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+3)+131072/1035*(4624106518*n^5+204906948227*n^4+3077030850953*n^3+20468514358942*n^2+62591864905626*n+72072677034504)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+4)+65536/1725*(459633013454*n^5+10686494860300*n^4+95044199592190*n^3+394611961602135*n^2+723639454901441*n+390570423733230)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+5)-16384/5175*(22252428179902*n^5+728772702954545*n^4+9602196417200105*n^3+63548559300612190*n^2+211012237923911778*n+280942969435624620)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+6)-8192/1725*(463954738906*n^5+58496329410920*n^4+1442525360983670*n^3+14704404926064115*n^2+68488421770314069*n+121032704218180260)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+7)+2048/5175*(75296589067046*n^5+3353733823804525*n^4+59012671074038755*n^3+513914288005106330*n^2+2218465475940804294*n+3802085173860464160)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+8)-1024/5175*(175835199949456*n^5+8210004220322225*n^4+153573772992273440*n^3+1438564975825879030*n^2+6747661796330515539*n+12677442553213349670)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+9)+512/1725*(47691619747724*n^5+2391125493634915*n^4+47926522426461715*n^3+479845148252368895*n^2+2398808567643373101*n+4788003291362148360)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+10)-512/345*(2780164758233*n^5+150213574335214*n^4+3237147465706754*n^3+34777507467601862*n^2+186244210729413050*n+397724882570176239)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+11)+256/5175*(9541083974626*n^5+557002188356735*n^4+13033073349114380*n^3+152895503433900160*n^2+900011606739133074*n+2128467569837601510)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+12)-64/575*(547852803396*n^5+37403673002705*n^4+1018627112613550*n^3+13833629275830135*n^2+93695354481967224*n+253206952707696630)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+13)+64/1725*(322835506114*n^5+22116001056755*n^4+604189699634700*n^3+8223943792908330*n^2+55740844638683286*n+150395619122828460)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+14)+16/5175*(257044162364*n^5+21601032477325*n^4+720168677105740*n^3+11920703915177375*n^2+98055655743052206*n+320886118254233790)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+15)-8/1725*(49219463984*n^5+3961387765405*n^4+127471130728165*n^3+2049913351279910*n^2+16474550727907356*n+52933591129761180)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+16)+4/5175*(4137428896*n^5+372951527030*n^4+13419854507630*n^3+240995080593505*n^2+2160254180206539*n+7733761194695400)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+17)-2/5175*(423777506*n^5+38903450095*n^4+1427528408905*n^3+26171679899375*n^2+239729565013239*n+877681300453200)/(n+20)/(n+19)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+18)-1/345*(1423042*n^4+110371909*n^3+3211837189*n^2+41561377584*n+201781947072)/(n+20)/(3*n+59)/(2*n+41)/(3*n+61)*a(n+19), n >= 20
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) = 109
a \! \left(6\right) = 522
a \! \left(7\right) = 2584
a \! \left(8\right) = 13140
a \! \left(9\right) = 68320
a \! \left(10\right) = 361656
a \! \left(11\right) = 1942474
a \! \left(12\right) = 10558944
a \! \left(13\right) = 57978138
a \! \left(14\right) = 321105516
a \! \left(15\right) = 1791691792
a \! \left(16\right) = 10062353548
a \! \left(17\right) = 56835384632
a \! \left(18\right) = 322656494440
a \! \left(19\right) = 1840046669608
a \! \left(n +20\right) = -\frac{66538438656 n \left(2 n +5\right) \left(2 n +3\right) \left(2 n +1\right) \left(n +2\right) a \! \left(n \right)}{115 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}-\frac{25165824 \left(2 n +5\right) \left(2 n +3\right) \left(826051 n^{3}+5251606 n^{2}+10766816 n +6331346\right) a \! \left(n +1\right)}{575 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}-\frac{1048576 \left(2 n +5\right) \left(419744543 n^{4}+4753917485 n^{3}+20140200060 n^{2}+37657506080 n +26055162252\right) a \! \left(n +2\right)}{575 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}-\frac{524288 \left(56243430352 n^{5}+950757418235 n^{4}+6347953992500 n^{3}+20877992358460 n^{2}+33734532761073 n +21351583420020\right) a \! \left(n +3\right)}{5175 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}+\frac{131072 \left(4624106518 n^{5}+204906948227 n^{4}+3077030850953 n^{3}+20468514358942 n^{2}+62591864905626 n +72072677034504\right) a \! \left(n +4\right)}{1035 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}+\frac{65536 \left(459633013454 n^{5}+10686494860300 n^{4}+95044199592190 n^{3}+394611961602135 n^{2}+723639454901441 n +390570423733230\right) a \! \left(n +5\right)}{1725 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}-\frac{16384 \left(22252428179902 n^{5}+728772702954545 n^{4}+9602196417200105 n^{3}+63548559300612190 n^{2}+211012237923911778 n +280942969435624620\right) a \! \left(n +6\right)}{5175 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}-\frac{8192 \left(463954738906 n^{5}+58496329410920 n^{4}+1442525360983670 n^{3}+14704404926064115 n^{2}+68488421770314069 n +121032704218180260\right) a \! \left(n +7\right)}{1725 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}+\frac{2048 \left(75296589067046 n^{5}+3353733823804525 n^{4}+59012671074038755 n^{3}+513914288005106330 n^{2}+2218465475940804294 n +3802085173860464160\right) a \! \left(n +8\right)}{5175 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}-\frac{1024 \left(175835199949456 n^{5}+8210004220322225 n^{4}+153573772992273440 n^{3}+1438564975825879030 n^{2}+6747661796330515539 n +12677442553213349670\right) a \! \left(n +9\right)}{5175 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}+\frac{512 \left(47691619747724 n^{5}+2391125493634915 n^{4}+47926522426461715 n^{3}+479845148252368895 n^{2}+2398808567643373101 n +4788003291362148360\right) a \! \left(n +10\right)}{1725 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}-\frac{512 \left(2780164758233 n^{5}+150213574335214 n^{4}+3237147465706754 n^{3}+34777507467601862 n^{2}+186244210729413050 n +397724882570176239\right) a \! \left(n +11\right)}{345 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}+\frac{256 \left(9541083974626 n^{5}+557002188356735 n^{4}+13033073349114380 n^{3}+152895503433900160 n^{2}+900011606739133074 n +2128467569837601510\right) a \! \left(n +12\right)}{5175 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}-\frac{64 \left(547852803396 n^{5}+37403673002705 n^{4}+1018627112613550 n^{3}+13833629275830135 n^{2}+93695354481967224 n +253206952707696630\right) a \! \left(n +13\right)}{575 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}+\frac{64 \left(322835506114 n^{5}+22116001056755 n^{4}+604189699634700 n^{3}+8223943792908330 n^{2}+55740844638683286 n +150395619122828460\right) a \! \left(n +14\right)}{1725 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}+\frac{16 \left(257044162364 n^{5}+21601032477325 n^{4}+720168677105740 n^{3}+11920703915177375 n^{2}+98055655743052206 n +320886118254233790\right) a \! \left(n +15\right)}{5175 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}-\frac{8 \left(49219463984 n^{5}+3961387765405 n^{4}+127471130728165 n^{3}+2049913351279910 n^{2}+16474550727907356 n +52933591129761180\right) a \! \left(n +16\right)}{1725 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}+\frac{4 \left(4137428896 n^{5}+372951527030 n^{4}+13419854507630 n^{3}+240995080593505 n^{2}+2160254180206539 n +7733761194695400\right) a \! \left(n +17\right)}{5175 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}-\frac{2 \left(423777506 n^{5}+38903450095 n^{4}+1427528408905 n^{3}+26171679899375 n^{2}+239729565013239 n +877681300453200\right) a \! \left(n +18\right)}{5175 \left(n +20\right) \left(n +19\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}-\frac{\left(1423042 n^{4}+110371909 n^{3}+3211837189 n^{2}+41561377584 n +201781947072\right) a \! \left(n +19\right)}{345 \left(n +20\right) \left(3 n +59\right) \left(2 n +41\right) \left(3 n +61\right)}, \quad n \geq 20
Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/24246/
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[21,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[21,x]*F[7,x]
F[7,x] = F[27,x]+F[8,x]
F[8,x] = F[0,x]*F[9,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[21,x]
F[12,x] = 1/F[21,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]+F[2,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[21,x]
F[17,x] = F[18,x]+F[22,x]
F[18,x] = F[19,x]*F[2,x]
F[19,x] = 1/F[21,x]*F[20,x]
F[20,x] = F[2,x]
F[21,x] = x
F[22,x] = -F[26,x]+F[23,x]
F[23,x] = 1/F[21,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[0,x]+F[19,x]
F[26,x] = F[0,x]*F[19,x]
F[27,x] = F[28,x]
F[28,x] = F[21,x]*F[29,x]*F[4,x]
F[29,x] = 1/F[21,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[21,x]*F[32,x]*F[9,x]
F[32,x] = 1/F[21,x]/F[4,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]+F[65,x]
F[35,x] = F[36,x]+F[63,x]
F[36,x] = F[37,x]
F[37,x] = F[21,x]*F[38,x]*F[4,x]
F[38,x] = F[0,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[21,x]*F[41,x]
F[41,x] = 1/F[21,x]/F[51,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[46,x]+F[44,x]
F[44,x] = 1/F[21,x]*F[45,x]
F[45,x] = F[10,x]
F[46,x] = -F[47,x]+F[12,x]
F[47,x] = F[48,x]
F[48,x] = F[21,x]*F[49,x]
F[49,x] = 1/F[0,x]/F[21,x]*F[50,x]
F[50,x] = F[22,x]
F[51,x] = F[52,x]+F[61,x]
F[52,x] = 1/F[0,x]/F[21,x]/F[38,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = -F[57,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[0,x]*F[21,x]*F[29,x]
F[57,x] = F[58,x]
F[58,x] = F[0,x]*F[21,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[38,x]^2*F[21,x]*F[4,x]
F[61,x] = F[62,x]
F[62,x] = -F[9,x]+F[52,x]
F[63,x] = F[64,x]
F[64,x] = F[21,x]*F[59,x]
F[65,x] = F[63,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_{21}\! \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_{21}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{27}\! \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) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{21}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{19}\! \left(x \right)
F_{26}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{21}\! \left(x \right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{21}\! \left(x \right) F_{32}\! \left(x \right) F_{9}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{21}\! \left(x \right) F_{4}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{65}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{63}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{21}\! \left(x \right) F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{0}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{21}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{21}\! \left(x \right) F_{51}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{10}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{12}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{21}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{0}\! \left(x \right) F_{21}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{22}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{61}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{0}\! \left(x \right) F_{21}\! \left(x \right) F_{38}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{0}\! \left(x \right) F_{21}\! \left(x \right) F_{29}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{0}\! \left(x \right) F_{21}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{38} \left(x \right)^{2} F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{9}\! \left(x \right)+F_{52}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{21}\! \left(x \right) F_{59}\! \left(x \right)
F_{65}\! \left(x \right) = F_{63}\! \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_21(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_21(x)*F_7(x))
Eq(F_7(x), F_27(x) + F_8(x))
Eq(F_8(x), F_0(x)*F_9(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_21(x))
Eq(F_12(x), F_13(x)/F_21(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x) + F_2(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_21(x))
Eq(F_17(x), F_18(x) + F_22(x))
Eq(F_18(x), F_19(x)*F_2(x))
Eq(F_19(x), F_20(x)/F_21(x))
Eq(F_20(x), F_2(x))
Eq(F_21(x), x)
Eq(F_22(x), F_23(x) - F_26(x))
Eq(F_23(x), F_24(x)/F_21(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), -F_0(x) + F_19(x))
Eq(F_26(x), F_0(x)*F_19(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_21(x)*F_29(x)*F_4(x))
Eq(F_29(x), F_30(x)/F_21(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_21(x)*F_32(x)*F_9(x))
Eq(F_32(x), F_33(x)/(F_21(x)*F_4(x)))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) + F_65(x))
Eq(F_35(x), F_36(x) + F_63(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_21(x)*F_38(x)*F_4(x))
Eq(F_38(x), F_0(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_21(x)*F_41(x))
Eq(F_41(x), F_42(x)/(F_21(x)*F_51(x)))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x) - F_46(x))
Eq(F_44(x), F_45(x)/F_21(x))
Eq(F_45(x), F_10(x))
Eq(F_46(x), F_12(x) - F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_21(x)*F_49(x))
Eq(F_49(x), F_50(x)/(F_0(x)*F_21(x)))
Eq(F_50(x), F_22(x))
Eq(F_51(x), F_52(x) + F_61(x))
Eq(F_52(x), F_53(x)/(F_0(x)*F_21(x)*F_38(x)))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_55(x) - F_57(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_0(x)*F_21(x)*F_29(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_0(x)*F_21(x)*F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_21(x)*F_38(x)**2*F_4(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_52(x) - F_9(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_21(x)*F_59(x))
Eq(F_65(x), F_63(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, 3, 4, 1], "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, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 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": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 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], [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], [0, 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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 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], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[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": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 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": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 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": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 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": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 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, 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], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], 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