01234_01243_01342_02341_10234_10243_10342_20134_20143
Counting sequence:
1, 1, 2, 6, 24, 111, 549, 2803, 14541, 76071, 399806, 2106743, 11117990, 58724996, 310345973, 1640607669, 8674513192, 45870675464, 242580271957, 1282904781857, 6784921494135, 35884120850658, 189786004142469, 1003757442868246, 5308784187981060, 28077757546687203, 148501358701653179, 785414375697684731, 4154009844799624866, 21970318705951110211, 116199776347179607570, 614574150411662283446, 3250448768020991011796, 17191445111755194093479, 90924612609583479984827, 480895311369735009306653, 2543429075866097758576778, 13452057777277672850916437, 71147200834050357870737468, 376293670743668848289263620, 1990196735775784029022590247, 10526042180452051477776544907, 55671664033669514492160172143, 294444400263010743536802396414, 1557300403339117212243818684307, 8236477053481495230167715239392, 43562278739637066116983274973768, 230398520704074166492345005997887, 1218565232965200009252514224119231, 6444925177496933351685087156373913, 34086858395976217074526045406881416, 180283538331228930587086127991336601, 953509819385957856871641214202842184, 5043061524455781029673378250412894806, 26672477851885404470538242231397874943, 141069283272157602425468146535895166821, 746107759214571288921915030208177244787, 3946123319298489270369193130782890299526, 20870831403007765380279812503603970418745, 110384691051360993835725990112566812879442, 583818621462204677773398776089111736991762, 3087784904944842325066912167471265910984483, 16331126258550061774609534721190985344913397, 86374437690046786650961209458786924064447027, 456829698586162231537969224779669106579038701, 2416147405313318314867605145261503444117299783, 12778872087929118491530628682188481312841718998, 67586758771626315856946627385586144104309330695, 357462687616055180537422477092339752650754332542, 1890600693982599221339878645235706049378779213948, 9999284143261967210257887940745701447098619509447, 52885669457286773036977663668351525848453531400379, 279709426582290931247513557714567939663741659268641, 1479367929381673690948748162280191849405678263034310, 7824296439430397908799981534510778882259602151251155, 41382277901393490578295092423492625388384682743614218, 218868614905494629502138311291137878527117745489275382, 1157584188690489933125885423554354485758030587533165361, 6122399753316867176437854417129151225092842592407802689, 32381038982415112023585554217764890107818903855210535943, 171261552304327871628195493221476658520487013055020503474, 905793026394741940839588592150849216704654017925639691791, 4790690003833449184992388316098971064194379333171712276520, 25337698617727958712800361727986150881208583892050434108972, 134009708565800071814315687268199051747063625081675866057347, 708770052909446128304551017973765977161725799424237443527273, 3748646223304018175811709506250916699843902762565316844243329, 19826385792977098005187333959621038908705651018546907445601816, 104860675080056588095817113412727410479995042414572875621947763, 554602401721654924747704693361481633144467332233138299961749286, 2933261909296319905902657728277187681530978299146570359821282960, 15513862546969094225300034287184683475089994154679589175034553619, 82051974412332206198524732874738293010400866796575105409144142707, 433968425630877832196505019598450816868813539711179759877890322211, 2295235377251780206087789288411736073032917510179701395993884297158, 12139374954133261919580605534484323238491198281018811567870004226679, 64204493246128851195472591043211523168642441149611663455265198388530, 339574069387209804993838628921862288498899060060344459520025449055764, 1795988766053256188306432652707917163184456052715183427207185982946811, 9498886807259230443446429673091314621371614591138094493268101395977163, 50239095189556387555820972434127986665932962785354240972675154514444459
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24418/
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[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[5,x]+F[67,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[64,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = F[12,x,1,k[0]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[47,x,k[0],k[1]]+F[49,x,k[0],k[1]]+F[58,x,k[1],k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[3,x]
F[14,x,k[0],k[1]] = 1/(-1+k[0])*(F[15,x,k[0],k[1]]*k[0]-F[15,x,1,k[1]])
F[15,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[16,x,k[0],k[1]]+F[18,x,k[0],k[1]]+F[40,x,k[1],k[0]]
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]*F[3,x]
F[17,x,k[0],k[1]] = (F[11,x,k[0]]*k[0]-F[11,x,k[1]]*k[1])/(-k[1]+k[0])
F[18,x,k[0],k[1]] = F[19,x,k[0]]*F[20,x,k[0],k[1]]
F[19,x,k[0]] = k[0]*x
F[20,x,k[0],k[1]] = (F[21,x,k[0],1]*k[0]-F[21,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[21,x,k[0],k[1]] = F[22,x,k[0],k[0]*k[1]]
F[22,x,k[0],k[1]] = F[1,x]+F[16,x,k[0],k[1]]+F[18,x,k[0],k[1]]+F[23,x,k[0],k[1]]+F[46,x,k[1]]
F[23,x,k[0],k[1]] = F[24,x,k[0],k[1]]*F[3,x]
F[24,x,k[0],k[1]] = F[1,x]+F[25,x,k[0],k[1]]+F[41,x,k[0],k[1]]+F[42,x,k[0],k[1]]+F[43,x,k[0],k[1]]+F[45,x,k[1]]
F[25,x,k[0],k[1]] = F[26,x,k[0],k[1]]*F[3,x]
F[26,x,k[0],k[1]] = F[27,x,1,k[0],k[1]]
F[27,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[28,x,k[0],k[1],k[2]]*k[0]-F[28,x,1,k[1],k[2]])
F[28,x,k[0],k[1],k[2]] = F[1,x]+F[29,x,k[0],k[1],k[2]]+F[31,x,k[0],k[1],k[2]]+F[33,x,k[0],k[1],k[2]]+F[37,x,k[1],k[0],k[2]]+F[40,x,k[2],k[0]]
F[29,x,k[0],k[1],k[2]] = F[3,x]*F[30,x,k[0],k[1],k[2]]
F[30,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[28,x,k[0],k[1],k[2]]*k[0]-F[28,x,1,k[1],k[2]])
F[31,x,k[0],k[1],k[2]] = F[3,x]*F[32,x,k[0],k[1],k[2]]
F[32,x,k[0],k[1],k[2]] = (F[17,x,k[0],k[2]]*k[0]-F[17,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[33,x,k[0],k[1],k[2]] = F[19,x,k[0]]*F[34,x,k[0],k[1],k[2]]
F[34,x,k[0],k[1],k[2]] = (F[35,x,k[0],1,k[2]]*k[0]-F[35,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[35,x,k[0],k[1],k[2]] = F[36,x,k[0],k[0]*k[1],k[2]]
F[36,x,k[0],k[1],k[2]] = (F[22,x,k[0],k[1]]*k[1]-F[22,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[37,x,k[0],k[1],k[2]] = F[19,x,k[0]]*F[38,x,k[1],k[0],k[2]]
F[38,x,k[0],k[1],k[2]] = (-F[39,x,1,k[1],k[2]]*k[1]+F[39,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[39,x,k[0],k[1],k[2]] = F[36,x,k[0]*k[1],k[1],k[2]]
F[40,x,k[0],k[1]] = F[19,x,k[0]]*F[7,x,k[1]]
F[41,x,k[0],k[1]] = F[31,x,1,k[0],k[1]]
F[42,x,k[0],k[1]] = F[33,x,1,k[0],k[1]]
F[43,x,k[0],k[1]] = F[19,x,k[0]]*F[44,x,k[0],k[1]]
F[44,x,k[0],k[1]] = F[38,x,1,k[0],k[1]]
F[45,x,k[0]] = F[40,x,k[0],1]
F[46,x,k[0]] = F[19,x,k[0]]*F[4,x]
F[47,x,k[0],k[1]] = F[3,x]*F[48,x,k[0],k[1]]
F[48,x,k[0],k[1]] = 1/(-1+k[0])*(F[12,x,k[0],k[1]]*k[0]-F[12,x,1,k[1]])
F[49,x,k[0],k[1]] = F[19,x,k[0]]*F[50,x,k[0],k[1]]
F[50,x,k[0],k[1]] = (F[51,x,k[0],1]*k[0]-F[51,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[51,x,k[0],k[1]] = F[52,x,k[0],k[0]*k[1]]
F[52,x,k[0],k[1]] = F[1,x]+F[49,x,k[0],k[1]]+F[53,x,k[0],k[1]]+F[55,x,k[0],k[1]]+F[57,x,k[1]]
F[53,x,k[0],k[1]] = F[3,x]*F[54,x,k[0],k[1]]
F[54,x,k[0],k[1]] = 1/(-1+k[0])*(F[22,x,k[0],k[1]]*k[0]-F[22,x,1,k[1]])
F[55,x,k[0],k[1]] = F[3,x]*F[56,x,k[0],k[1]]
F[56,x,k[0],k[1]] = 1/(-1+k[0])*(F[52,x,k[0],k[1]]*k[0]-F[52,x,1,k[1]])
F[57,x,k[0]] = F[0,x]*F[19,x,k[0]]
F[58,x,k[0],k[1]] = F[19,x,k[0]]*F[59,x,k[1]]
F[59,x,k[0]] = F[1,x]+F[60,x,k[0]]+F[62,x,k[0]]+F[8,x,k[0]]
F[60,x,k[0]] = F[3,x]*F[61,x,k[0]]
F[61,x,k[0]] = 1/(-1+k[0])*(F[59,x,k[0]]*k[0]-F[59,x,1])
F[62,x,k[0]] = F[19,x,k[0]]*F[63,x,k[0]]
F[63,x,k[0]] = F[51,x,k[0],1]
F[64,x,k[0]] = F[19,x,k[0]]*F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,1,k[0]]
F[66,x,k[0],k[1]] = F[22,x,k[0]*k[1],k[1]]
F[67,x] = F[3,x]*F[68,x]
F[68,x] = F[59,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_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{67}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{64}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , 1, y_{0}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{47}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)+F_{58}\! \left(x , y_{1}, y_{0}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{15}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{15}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{1}, y_{0}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{11}\! \left(x , y_{0}\right) y_{0}-F_{11}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{0}, y_{1}\right)
F_{19}\! \left(x , y_{0}\right) = y_{0} x
F_{20}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{21}\! \left(x , y_{0}, 1\right) y_{0}-F_{21}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{1}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{43}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{1}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , 1, y_{0}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{28}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{37}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{40}\! \left(x , y_{2}, y_{0}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{3}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{28}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{3}\! \left(x \right) F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{17}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{17}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}\right) F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{35}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{35}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{36}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{22}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{22}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}\right) F_{38}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{39}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-F_{39}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{36}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{7}\! \left(x , y_{1}\right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , 1, y_{0}, y_{1}\right)
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , 1, y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{44}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{38}\! \left(x , 1, y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}\right) = F_{40}\! \left(x , y_{0}, 1\right)
F_{46}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{48}\! \left(x , y_{0}, y_{1}\right)
F_{48}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{12}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{12}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{49}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{50}\! \left(x , y_{0}, y_{1}\right)
F_{50}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{51}\! \left(x , y_{0}, 1\right)-F_{51}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{52}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{49}\! \left(x , y_{0}, y_{1}\right)+F_{53}\! \left(x , y_{0}, y_{1}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)+F_{57}\! \left(x , y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{54}\! \left(x , y_{0}, y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{22}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{22}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{55}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{56}\! \left(x , y_{0}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{52}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{52}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{57}\! \left(x , y_{0}\right) = F_{0}\! \left(x \right) F_{19}\! \left(x , y_{0}\right)
F_{58}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}\right) F_{59}\! \left(x , y_{1}\right)
F_{59}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{60}\! \left(x , y_{0}\right)+F_{62}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{61}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{59}\! \left(x , y_{0}\right)+F_{59}\! \left(x , 1\right)}{-1+y_{0}}
F_{62}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{63}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}, 1\right)
F_{64}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{65}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{66}\! \left(x , 1, y_{0}\right)
F_{66}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{67}\! \left(x \right) = F_{3}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{59}\! \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_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_5(x) + F_67(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_64(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), F_12(x, 1, k_0))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_47(x, k_0, k_1) + F_49(x, k_0, k_1) + F_58(x, k_1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_3(x))
Eq(F_14(x, k_0, k_1), (k_0*F_15(x, k_0, k_1) - F_15(x, 1, k_1))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_16(x, k_0, k_1) + F_18(x, k_0, k_1) + F_40(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1)*F_3(x))
Eq(F_17(x, k_0, k_1), (-k_0*F_11(x, k_0) + k_1*F_11(x, k_1))/(-k_0 + k_1))
Eq(F_18(x, k_0, k_1), F_19(x, k_0)*F_20(x, k_0, k_1))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x, k_0, k_1), (-k_0*F_21(x, k_0, 1) + k_1*F_21(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_0*k_1))
Eq(F_22(x, k_0, k_1), F_1(x) + F_16(x, k_0, k_1) + F_18(x, k_0, k_1) + F_23(x, k_0, k_1) + F_46(x, k_1))
Eq(F_23(x, k_0, k_1), F_24(x, k_0, k_1)*F_3(x))
Eq(F_24(x, k_0, k_1), F_1(x) + F_25(x, k_0, k_1) + F_41(x, k_0, k_1) + F_42(x, k_0, k_1) + F_43(x, k_0, k_1) + F_45(x, k_1))
Eq(F_25(x, k_0, k_1), F_26(x, k_0, k_1)*F_3(x))
Eq(F_26(x, k_0, k_1), F_27(x, 1, k_0, k_1))
Eq(F_27(x, k_0, k_1, k_2), (-k_0*F_28(x, k_0, k_1, k_2) + F_28(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_28(x, k_0, k_1, k_2), F_1(x) + F_29(x, k_0, k_1, k_2) + F_31(x, k_0, k_1, k_2) + F_33(x, k_0, k_1, k_2) + F_37(x, k_1, k_0, k_2) + F_40(x, k_2, k_0))
Eq(F_29(x, k_0, k_1, k_2), F_3(x)*F_30(x, k_0, k_1, k_2))
Eq(F_30(x, k_0, k_1, k_2), (k_0*F_28(x, k_0, k_1, k_2) - F_28(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_31(x, k_0, k_1, k_2), F_3(x)*F_32(x, k_0, k_1, k_2))
Eq(F_32(x, k_0, k_1, k_2), (-k_0*F_17(x, k_0, k_2) + k_1*F_17(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_33(x, k_0, k_1, k_2), F_19(x, k_0)*F_34(x, k_0, k_1, k_2))
Eq(F_34(x, k_0, k_1, k_2), (-k_0*F_35(x, k_0, 1, k_2) + k_1*F_35(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_35(x, k_0, k_1, k_2), F_36(x, k_0, k_0*k_1, k_2))
Eq(F_36(x, k_0, k_1, k_2), (-k_1*F_22(x, k_0, k_1) + k_2*F_22(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_37(x, k_0, k_1, k_2), F_19(x, k_0)*F_38(x, k_1, k_0, k_2))
Eq(F_38(x, k_0, k_1, k_2), (-k_0*F_39(x, k_0/k_1, k_1, k_2) + k_1*F_39(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_39(x, k_0, k_1, k_2), F_36(x, k_0*k_1, k_1, k_2))
Eq(F_40(x, k_0, k_1), F_19(x, k_0)*F_7(x, k_1))
Eq(F_41(x, k_0, k_1), F_31(x, 1, k_0, k_1))
Eq(F_42(x, k_0, k_1), F_33(x, 1, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_19(x, k_0)*F_44(x, k_0, k_1))
Eq(F_44(x, k_0, k_1), F_38(x, 1, k_0, k_1))
Eq(F_45(x, k_0), F_40(x, k_0, 1))
Eq(F_46(x, k_0), F_19(x, k_0)*F_4(x))
Eq(F_47(x, k_0, k_1), F_3(x)*F_48(x, k_0, k_1))
Eq(F_48(x, k_0, k_1), (k_0*F_12(x, k_0, k_1) - F_12(x, 1, k_1))/(k_0 - 1))
Eq(F_49(x, k_0, k_1), F_19(x, k_0)*F_50(x, k_0, k_1))
Eq(F_50(x, k_0, k_1), (-k_0*F_51(x, k_0, 1) + k_1*F_51(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_51(x, k_0, k_1), F_52(x, k_0, k_0*k_1))
Eq(F_52(x, k_0, k_1), F_1(x) + F_49(x, k_0, k_1) + F_53(x, k_0, k_1) + F_55(x, k_0, k_1) + F_57(x, k_1))
Eq(F_53(x, k_0, k_1), F_3(x)*F_54(x, k_0, k_1))
Eq(F_54(x, k_0, k_1), (k_0*F_22(x, k_0, k_1) - F_22(x, 1, k_1))/(k_0 - 1))
Eq(F_55(x, k_0, k_1), F_3(x)*F_56(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), (k_0*F_52(x, k_0, k_1) - F_52(x, 1, k_1))/(k_0 - 1))
Eq(F_57(x, k_0), F_0(x)*F_19(x, k_0))
Eq(F_58(x, k_0, k_1), F_19(x, k_0)*F_59(x, k_1))
Eq(F_59(x, k_0), F_1(x) + F_60(x, k_0) + F_62(x, k_0) + F_8(x, k_0))
Eq(F_60(x, k_0), F_3(x)*F_61(x, k_0))
Eq(F_61(x, k_0), (k_0*F_59(x, k_0) - F_59(x, 1))/(k_0 - 1))
Eq(F_62(x, k_0), F_19(x, k_0)*F_63(x, k_0))
Eq(F_63(x, k_0), F_51(x, k_0, 1))
Eq(F_64(x, k_0), F_19(x, k_0)*F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, 1, k_0))
Eq(F_66(x, k_0, k_1), F_22(x, k_0*k_1, k_1))
Eq(F_67(x), F_3(x)*F_68(x))
Eq(F_68(x), F_59(x, 1))
Pack JSON:
{"name": "col_placements_tracked_fusion", "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", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"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": [0, 2, 3, 4, 1], "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": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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": [0, 2, 3, 4, 1], "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": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 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