01234_01243_01342_10234_10243_10342_20134_20143
Counting sequence:
1, 1, 2, 6, 24, 112, 563, 2932, 15536, 83048, 445982, 2400927, 12942798, 69823762, 376843039, 2034323388, 10983401011, 59304234608, 320222809514, 1729133144666, 9337050163802, 50418918129899, 272256690015336, 1470158238622170, 7938706060512465, 42868206031242272, 231483892317180919, 1249988758130385791, 6749806310896984196, 36448226819640946774, 196816457376745148477, 1062787274344316685051, 5738933953753653632061, 30989606870212706488578, 167340428365731154497253, 903619643142704717367978, 4879445069298154951587077, 26348457225765909498409790, 142278716975273890993956536, 768289119616246002623655498, 4148675062480106349948192390, 22402379785018834951167648451, 120970336244845802777487931650, 653226234631516751356934148040, 3527348320758724083567907597241, 19047284832510874705443981991564, 102853199055922307932440334355705, 555395723766105984014423840714345, 2999074531344051560259695764737078, 16194665632234625461599042004098406, 87449375500301686399180410112902803, 472216805650326830627177896723957559, 2549917712073847193844513722595798063, 13769269241815879748871247519139839229, 74352507352917099223275199358660501363, 401495188467901547255288894934635011748, 2168028921881040481648045749381508527980, 11707112665277037265354513764513294596008, 63217093448842249137066621724568212847955, 341365204070170299930113515848995997711105, 1843333759765950245135128467550597044685648, 9953795259011721436514823744318067394423481, 53749376385497088163573722796185698186779437, 290240595334978517648618514022524542315274025, 1567266614890239875154004078350701579100550042, 8463063684490933646472045791364586000870463418, 45699593322008848956129029095643340652343826232, 246772670944455229560834337202443901230440247749, 1332544705505907655179778731474821029827627626093, 7195591737833022136212717223479451530138017872256, 38855387172841340302947886130372251756809294639889, 209814726482199621892385840265805526001944807860765, 1132975956537687713404367796473816476049670629059435, 6117942909032279145859626230855425795210943553884392, 33036204539200038918727081051272521920063644615318461, 178391793873150508425149255877407482660483888325374000, 963295649883687383854523885415930257886855912598975741, 5201688311653147877962738897678510435742913156701220990, 28088532627397813043444672812140942774481827139691213052, 151674921273711819573680903834904672087313385736347270366, 819027538695518688551580478788416412727243434151768592516, 4422656715483637530749827345409728387660472700300326959323, 23881849509194555011856454723962840895405489508825172160338, 128959304931593400384824103513856715649972299529956416059642, 696365761874383516517277517480529547352254273758697069228837, 3760296898065003215609701016560328999878967846285742047213310, 20305180891630235395736293177427403688442803636145098213112903, 109645696129470320917774094129199901013423226785465364516201969, 592074443654508735086907914946488487210475168640805111302390246, 3197135493716613182673983812351046916532155318786699301269023174, 17264172562643471487869456638738626057682868685340642938897182361, 93224592720107652278174328323711917630388480302926675552125934849, 503402329668281371034924132039822302876556558854908161333243073071, 2718316037875208082580868795433843791809763104693447379948101403563, 14678601282276016483837967639264526375688228526795219955445606871661, 79262798218433810872480053267978074416691424708347989659585169207630, 428010207553099737088252461315965501315748192932218738460317006349700, 2311207046523915861592734467556549772315473717562052822783144593905168, 12480258455609621375348251588470318848860093960213170197432243112129303, 67391993873104397751058377132890628825199621617598139827978191870653311, 363909197421400179947704153831947521226686975477029415406996938282297934
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24150/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[27,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[64,x]
F[4,x] = F[27,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[52,x,k[0]]+F[62,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[12,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = F[9,x,1,k[0]]
F[9,x,k[0],k[1]] = F[10,x,k[0]*k[1],k[1]]
F[10,x,k[0],k[1]] = F[1,x]+F[11,x,k[0]]+F[13,x,k[0],k[1]]+F[15,x,k[0],k[1]]+F[49,x,k[0],k[1]]
F[11,x,k[0]] = F[12,x,k[0]]*F[3,x]
F[12,x,k[0]] = k[0]*x
F[13,x,k[0],k[1]] = F[12,x,k[1]]*F[14,x,k[0],k[1]]
F[14,x,k[0],k[1]] = (-F[9,x,1,k[1]]*k[1]+F[9,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[27,x]
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1],1]
F[17,x,k[0],k[1],k[2]] = F[1,x]+F[18,x,k[2],k[0]]+F[19,x,k[0],k[1],k[2]]+F[23,x,k[0],k[1],k[2]]+F[25,x,k[0],k[1],k[2]]+F[28,x,k[0],k[1],k[2]]
F[18,x,k[0],k[1]] = F[12,x,k[1]]*F[6,x,k[0]]
F[19,x,k[0],k[1],k[2]] = F[12,x,k[1]]*F[20,x,k[0],k[1],k[2]]
F[20,x,k[0],k[1],k[2]] = (-F[21,x,1,k[1],k[2]]*k[1]+F[21,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[21,x,k[0],k[1],k[2]] = (F[22,x,k[0],k[1],1]*k[1]-F[22,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[22,x,k[0],k[1],k[2]] = F[10,x,k[0]*k[1],k[1]*k[2]]
F[23,x,k[0],k[1],k[2]] = F[12,x,k[2]]*F[24,x,k[0],k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = (F[14,x,k[0],k[2]]*k[0]-F[14,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[25,x,k[0],k[1],k[2]] = F[26,x,k[0],k[1],k[2]]*F[27,x]
F[26,x,k[0],k[1],k[2]] = (F[17,x,k[0],k[1],k[2]]*k[2]-F[17,x,k[0],k[1],1])/(-1+k[2])
F[27,x] = x
F[28,x,k[0],k[1],k[2]] = F[27,x]*F[29,x,k[0],k[1],k[2]]
F[29,x,k[0],k[1],k[2]] = (F[30,x,k[0],k[1],k[2]]*k[2]-F[30,x,k[0],k[1],1])/(-1+k[2])
F[30,x,k[0],k[1],k[2]] = F[1,x]+F[28,x,k[0],k[1],k[2]]+F[31,x,k[2],k[0]]+F[54,x,k[0],k[1],k[2]]+F[58,x,k[0],k[1],k[2]]+F[60,x,k[0],k[1],k[2]]
F[31,x,k[0],k[1]] = F[12,x,k[1]]*F[32,x,k[0]]
F[32,x,k[0]] = F[1,x]+F[33,x,k[0]]+F[51,x,k[0]]+F[52,x,k[0]]
F[33,x,k[0]] = F[12,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0],1]
F[35,x,k[0],k[1]] = F[36,x,k[0],k[0]*k[1]]
F[36,x,k[0],k[1]] = F[1,x]+F[11,x,k[0]]+F[37,x,k[0],k[1]]+F[40,x,k[0],k[1]]+F[49,x,k[0],k[1]]
F[37,x,k[0],k[1]] = F[12,x,k[1]]*F[38,x,k[0],k[1]]
F[38,x,k[0],k[1]] = (-F[39,x,1,k[1]]*k[1]+F[39,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[39,x,k[0],k[1]] = F[36,x,k[0]*k[1],k[1]]
F[40,x,k[0],k[1]] = F[27,x]*F[41,x,k[0],k[1]]
F[41,x,k[0],k[1]] = (F[42,x,k[0]]*k[0]-F[42,x,k[1]]*k[1])/(-k[1]+k[0])
F[42,x,k[0]] = F[43,x,k[0],1]
F[43,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[18,x,k[1],k[0]]+F[44,x,k[0],k[1]]+F[46,x,k[0],k[1]]
F[44,x,k[0],k[1]] = F[27,x]*F[45,x,k[0],k[1]]
F[45,x,k[0],k[1]] = (F[43,x,k[0],k[1]]*k[1]-F[43,x,k[0],1])/(-1+k[1])
F[46,x,k[0],k[1]] = F[27,x]*F[47,x,k[0],k[1]]
F[47,x,k[0],k[1]] = (F[48,x,k[0],k[1]]*k[1]-F[48,x,k[0],1])/(-1+k[1])
F[48,x,k[0],k[1]] = F[1,x]+F[31,x,k[1],k[0]]+F[37,x,k[0],k[1]]+F[40,x,k[0],k[1]]+F[46,x,k[0],k[1]]
F[49,x,k[0],k[1]] = F[27,x]*F[50,x,k[0],k[1]]
F[50,x,k[0],k[1]] = F[30,x,k[0],k[1],1]
F[51,x,k[0]] = F[27,x]*F[42,x,k[0]]
F[52,x,k[0]] = F[27,x]*F[53,x,k[0]]
F[53,x,k[0]] = (F[32,x,k[0]]*k[0]-F[32,x,1])/(-1+k[0])
F[54,x,k[0],k[1],k[2]] = F[12,x,k[1]]*F[55,x,k[0],k[1],k[2]]
F[55,x,k[0],k[1],k[2]] = (-F[56,x,1,k[1],k[2]]*k[1]+F[56,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[56,x,k[0],k[1],k[2]] = (F[57,x,k[0],k[1],1]*k[1]-F[57,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[57,x,k[0],k[1],k[2]] = F[36,x,k[0]*k[1],k[1]*k[2]]
F[58,x,k[0],k[1],k[2]] = F[12,x,k[2]]*F[59,x,k[0],k[1],k[2]]
F[59,x,k[0],k[1],k[2]] = (F[38,x,k[0],k[2]]*k[0]-F[38,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[60,x,k[0],k[1],k[2]] = F[27,x]*F[61,x,k[0],k[1],k[2]]
F[61,x,k[0],k[1],k[2]] = (F[41,x,k[0],k[2]]*k[0]-F[41,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[62,x,k[0]] = F[27,x]*F[63,x,k[0]]
F[63,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[64,x] = F[27,x]*F[65,x]
F[65,x] = F[32,x,1]
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_{27}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{64}\! \left(x \right)
F_{4}\! \left(x \right) = F_{27}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{52}\! \left(x , y_{0}\right)+F_{62}\! \left(x , y_{0}\right)+F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{9}\! \left(x , 1, y_{0}\right)
F_{9}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{12}\! \left(x , y_{0}\right) = y_{0} x
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{1}\right) F_{14}\! \left(x , y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = \frac{-y_{1} F_{9}\! \left(x , 1, y_{1}\right)+y_{0} F_{9}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{0}, y_{1}\right) F_{27}\! \left(x \right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0}, y_{1}, 1\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y_{2}, y_{0}\right)+F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{1}\right) F_{6}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{1}\right) F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-y_{1} F_{21}\! \left(x , 1, y_{1}, y_{2}\right)+y_{0} F_{21}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{22}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{22}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{2}\right) F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{14}\! \left(x , y_{0}, y_{2}\right)-y_{1} F_{14}\! \left(x , y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{27}\! \left(x \right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{2} F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{17}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{27}\! \left(x \right) = x
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x \right) F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{2} F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{30}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{31}\! \left(x , y_{2}, y_{0}\right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{1}\right) F_{32}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y_{0}\right)+F_{51}\! \left(x , y_{0}\right)+F_{52}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{35}\! \left(x , y_{0}, 1\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{1}\right) F_{38}\! \left(x , y_{0}, y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = \frac{-y_{1} F_{39}\! \left(x , 1, y_{1}\right)+y_{0} F_{39}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x \right) F_{41}\! \left(x , y_{0}, y_{1}\right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{42}\! \left(x , y_{0}\right)-y_{1} F_{42}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{42}\! \left(x , y_{0}\right) = F_{43}\! \left(x , y_{0}, 1\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{1}, y_{0}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x \right) F_{45}\! \left(x , y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{1} F_{43}\! \left(x , y_{0}, y_{1}\right)-F_{43}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x \right) F_{47}\! \left(x , y_{0}, y_{1}\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{1} F_{48}\! \left(x , y_{0}, y_{1}\right)-F_{48}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{48}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y_{1}, y_{0}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)
F_{49}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x \right) F_{50}\! \left(x , y_{0}, y_{1}\right)
F_{50}\! \left(x , y_{0}, y_{1}\right) = F_{30}\! \left(x , y_{0}, y_{1}, 1\right)
F_{51}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{42}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{53}\! \left(x , y_{0}\right)
F_{53}\! \left(x , y_{0}\right) = \frac{y_{0} F_{32}\! \left(x , y_{0}\right)-F_{32}\! \left(x , 1\right)}{-1+y_{0}}
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{1}\right) F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-y_{1} F_{56}\! \left(x , 1, y_{1}, y_{2}\right)+y_{0} F_{56}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{57}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{57}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{36}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{2}\right) F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{38}\! \left(x , y_{0}, y_{2}\right)-y_{1} F_{38}\! \left(x , y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x \right) F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{41}\! \left(x , y_{0}, y_{2}\right)-y_{1} F_{41}\! \left(x , y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{62}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{63}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = \frac{y_{0} F_{6}\! \left(x , y_{0}\right)-F_{6}\! \left(x , 1\right)}{-1+y_{0}}
F_{64}\! \left(x \right) = F_{27}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{32}\! \left(x , 1\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_27(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_64(x))
Eq(F_4(x), F_27(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_52(x, k_0) + F_62(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_12(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), F_9(x, 1, k_0))
Eq(F_9(x, k_0, k_1), F_10(x, k_0*k_1, k_1))
Eq(F_10(x, k_0, k_1), F_1(x) + F_11(x, k_0) + F_13(x, k_0, k_1) + F_15(x, k_0, k_1) + F_49(x, k_0, k_1))
Eq(F_11(x, k_0), F_12(x, k_0)*F_3(x))
Eq(F_12(x, k_0), k_0*x)
Eq(F_13(x, k_0, k_1), F_12(x, k_1)*F_14(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), (-k_0*F_9(x, k_0/k_1, k_1) + k_1*F_9(x, 1, k_1))/(-k_0 + k_1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_27(x))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1, 1))
Eq(F_17(x, k_0, k_1, k_2), F_1(x) + F_18(x, k_2, k_0) + F_19(x, k_0, k_1, k_2) + F_23(x, k_0, k_1, k_2) + F_25(x, k_0, k_1, k_2) + F_28(x, k_0, k_1, k_2))
Eq(F_18(x, k_0, k_1), F_12(x, k_1)*F_6(x, k_0))
Eq(F_19(x, k_0, k_1, k_2), F_12(x, k_1)*F_20(x, k_0, k_1, k_2))
Eq(F_20(x, k_0, k_1, k_2), (-k_0*F_21(x, k_0/k_1, k_1, k_2) + k_1*F_21(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_21(x, k_0, k_1, k_2), (-k_1*F_22(x, k_0, k_1, 1) + k_2*F_22(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_22(x, k_0, k_1, k_2), F_10(x, k_0*k_1, k_1*k_2))
Eq(F_23(x, k_0, k_1, k_2), F_12(x, k_2)*F_24(x, k_0, k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), (-k_0*F_14(x, k_0, k_2) + k_1*F_14(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1, k_2), F_26(x, k_0, k_1, k_2)*F_27(x))
Eq(F_26(x, k_0, k_1, k_2), (-k_2*F_17(x, k_0, k_1, k_2) + F_17(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_27(x), x)
Eq(F_28(x, k_0, k_1, k_2), F_27(x)*F_29(x, k_0, k_1, k_2))
Eq(F_29(x, k_0, k_1, k_2), (-k_2*F_30(x, k_0, k_1, k_2) + F_30(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_30(x, k_0, k_1, k_2), F_1(x) + F_28(x, k_0, k_1, k_2) + F_31(x, k_2, k_0) + F_54(x, k_0, k_1, k_2) + F_58(x, k_0, k_1, k_2) + F_60(x, k_0, k_1, k_2))
Eq(F_31(x, k_0, k_1), F_12(x, k_1)*F_32(x, k_0))
Eq(F_32(x, k_0), F_1(x) + F_33(x, k_0) + F_51(x, k_0) + F_52(x, k_0))
Eq(F_33(x, k_0), F_12(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0, 1))
Eq(F_35(x, k_0, k_1), F_36(x, k_0, k_0*k_1))
Eq(F_36(x, k_0, k_1), F_1(x) + F_11(x, k_0) + F_37(x, k_0, k_1) + F_40(x, k_0, k_1) + F_49(x, k_0, k_1))
Eq(F_37(x, k_0, k_1), F_12(x, k_1)*F_38(x, k_0, k_1))
Eq(F_38(x, k_0, k_1), (-k_0*F_39(x, k_0/k_1, k_1) + k_1*F_39(x, 1, k_1))/(-k_0 + k_1))
Eq(F_39(x, k_0, k_1), F_36(x, k_0*k_1, k_1))
Eq(F_40(x, k_0, k_1), F_27(x)*F_41(x, k_0, k_1))
Eq(F_41(x, k_0, k_1), (-k_0*F_42(x, k_0) + k_1*F_42(x, k_1))/(-k_0 + k_1))
Eq(F_42(x, k_0), F_43(x, k_0, 1))
Eq(F_43(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_18(x, k_1, k_0) + F_44(x, k_0, k_1) + F_46(x, k_0, k_1))
Eq(F_44(x, k_0, k_1), F_27(x)*F_45(x, k_0, k_1))
Eq(F_45(x, k_0, k_1), (-k_1*F_43(x, k_0, k_1) + F_43(x, k_0, 1))/(1 - k_1))
Eq(F_46(x, k_0, k_1), F_27(x)*F_47(x, k_0, k_1))
Eq(F_47(x, k_0, k_1), (-k_1*F_48(x, k_0, k_1) + F_48(x, k_0, 1))/(1 - k_1))
Eq(F_48(x, k_0, k_1), F_1(x) + F_31(x, k_1, k_0) + F_37(x, k_0, k_1) + F_40(x, k_0, k_1) + F_46(x, k_0, k_1))
Eq(F_49(x, k_0, k_1), F_27(x)*F_50(x, k_0, k_1))
Eq(F_50(x, k_0, k_1), F_30(x, k_0, k_1, 1))
Eq(F_51(x, k_0), F_27(x)*F_42(x, k_0))
Eq(F_52(x, k_0), F_27(x)*F_53(x, k_0))
Eq(F_53(x, k_0), (-k_0*F_32(x, k_0) + F_32(x, 1))/(1 - k_0))
Eq(F_54(x, k_0, k_1, k_2), F_12(x, k_1)*F_55(x, k_0, k_1, k_2))
Eq(F_55(x, k_0, k_1, k_2), (-k_0*F_56(x, k_0/k_1, k_1, k_2) + k_1*F_56(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_56(x, k_0, k_1, k_2), (-k_1*F_57(x, k_0, k_1, 1) + k_2*F_57(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_57(x, k_0, k_1, k_2), F_36(x, k_0*k_1, k_1*k_2))
Eq(F_58(x, k_0, k_1, k_2), F_12(x, k_2)*F_59(x, k_0, k_1, k_2))
Eq(F_59(x, k_0, k_1, k_2), (-k_0*F_38(x, k_0, k_2) + k_1*F_38(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_60(x, k_0, k_1, k_2), F_27(x)*F_61(x, k_0, k_1, k_2))
Eq(F_61(x, k_0, k_1, k_2), (-k_0*F_41(x, k_0, k_2) + k_1*F_41(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_62(x, k_0), F_27(x)*F_63(x, k_0))
Eq(F_63(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_64(x), F_27(x)*F_65(x))
Eq(F_65(x), F_32(x, 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": false, "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": "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, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3, 4], "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]]}], "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, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3, 4], "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]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], 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