01234_01243_02134_02143
Counting sequence:
1, 1, 2, 6, 24, 116, 632, 3728, 23268, 151484, 1018824, 7030256, 49522764, 354794596, 2577806856, 18952296240, 140749625076, 1054364552748, 7957739301832, 60454536765008, 461915265713788, 3547308019493364, 27364774607076360, 211948559331862864, 1647530487039159748, 12848253040477531932, 100490721232091656008, 788061063518931903536, 6194996375999484950956, 48806436711028293911684, 385288573577898844660616, 3047160510902842116133872, 24140137181632040298371604, 191540740338475802374210444, 1521974471074217951882678088, 12109641623629134244368523152, 96469588045596830680016292572, 769389537181211474483551499028, 6142765067862211093851462203528, 49092089972487245274762493800720, 392699305318203714988697329384164, 3144005162385520062899458957643900, 25191650372126167517871508771339208, 202003081340606330853064562999671408, 1620939954668078053262683252965336844, 13015612167474459024579044588532647076, 104576392571373045052481026464176424712, 840732959064540048562181356963093482160, 6762745243416171121594771227713989226292, 54427049390751176794000527557949478386412, 438248693407486963758030960530306706150600, 3530439056630657868565282527125263614349008, 28452999805814582796125225464078437415512892, 229407924995800745129091863491019724817602612, 1850377086944709535404618615205838257897687816, 14930509545062509156345424046152366793516882640, 120515597332075606431732016531862366602618410500, 973101952116130591586309622451488877720688789468, 7859820023448713039649683721516787545546821134920, 63503725272620420714079894860764799339685376157360, 513229654779732386914134175799016140524756993033324, 4149007371250927544448535655832178665360272277748932, 33549877884612355012183619056153503612831787050594440, 271360505027195762416390908351581093023535325741812592, 2195362734415476079438852650420196149611720050286759508, 17764998569865780246231641944495614816253650848991124556, 143786747796062708252290050234310403628327318984532048968, 1164027245806538302100595547305745424698257189074343017488, 9425275882259474851206315207556161346682992152741510139804, 76332220149238296890302389091774922228490846367912928842068, 618302604389256084692856995587938337514450944563249264186248, 5009221856075447969029735752282617691415416858014418429867664, 40589368608729471917235933929749951117651880989463115584010020, 328945657266704827758441468409532974316999682089955507821247804, 2666263099266116930814389719174795348694500552507293009841896136, 21614546459212549377849844592773165123062344365495245793801140464, 175247150803678698153367637308667214400928026055687525980210526668, 1421068722468248771638515376899319951991430207291829456992445015268, 11524873180774260905830424049077119254204058125444344709170857852936, 93478554005590720844770116980719626340032733320047676974235139860016, 758298988363928007071709516017148073926974307490121292510965104504692, 6152046821229124797180525503360619394242907331243888761567159461728172, 49916893697783938007505724070460931112069499657116841157834427529840072, 405062859225505835378616182353190250630523669588867672237889603972478800, 3287324089739795597699511154598913966687294912085037069220108089105620988, 26681251675128680947329023154376787804218692976349175140200502441427097204, 216576775444682216196853394792860408798918642993384635096637886408544498184, 1758158696224613602357944360225730555725266363737108133654007039270656824400, 14273922521501973768671797836437373506074881090311562560918897975159556003396, 115895426792400063107890208849795619248846490542251415682173336593598582429852, 941078074837948461320925869036055448316310655607615116288150584462496377843016, 7642230825109244534533039791359738472346087805284473888141811829175753662693680, 62065261133538422488420772345117583189363117309867512637038043599627633899958060, 504092012472549395550579527917931598831885959422463788400728018262216349548541188, 4094517567687233671269120060039694740116137545480681382881094242780075278153471368, 33260310770734712186705010603873739462112291517003943339267556986666107742418479856, 270196362947525918836716683305116514197926654431411452087013215987362006987125082772, 2195135632242317162487510635144991497943886725075083214542572951485793918479615786252, 17834911427775723902713714420933404000651877416911975646239184407671999492838769324360, 144913017858707116798442807455835988426049315645061387630503741794104232282561607438480, 1177524188111891759930104819730319638747824080580594214505689496218202045000950989079644
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/24056/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[7,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[8,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0]]*F[7,x]
F[6,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[7,x] = x
F[8,x,k[0]] = F[21,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,1,k[0]]
F[10,x,k[0],k[1]] = F[11,x,k[0]*k[1],k[1]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[51,x,k[0],k[1]]+F[52,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[7,x]
F[13,x,k[0],k[1]] = F[14,x,1,k[0],k[1]]
F[14,x,k[0],k[1],k[2]] = F[1,x]+F[15,x,k[0],k[1],k[2]]+F[17,x,k[0],k[1],k[2]]+F[22,x,k[0],k[1],k[2]]+F[49,x,k[0],k[1],k[2]]
F[15,x,k[0],k[1],k[2]] = F[16,x,k[0],k[1],k[2]]*F[7,x]
F[16,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[14,x,k[0],k[1],k[2]]*k[0]-F[14,x,1,k[1],k[2]])
F[17,x,k[0],k[1],k[2]] = F[18,x,k[0],k[1],k[2]]*F[21,x,k[0]]
F[18,x,k[0],k[1],k[2]] = (F[19,x,k[0],k[1]]*k[1]-F[19,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[19,x,k[0],k[1]] = (F[20,x,k[0],1]*k[0]-F[20,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1]] = F[11,x,k[0],k[0]*k[1]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0],k[1],k[2]] = F[21,x,k[1]]*F[23,x,k[0],k[1],k[2]]
F[23,x,k[0],k[1],k[2]] = (-F[24,x,1,k[1],k[2]]*k[1]+F[24,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[24,x,k[0],k[1],k[2]] = F[25,x,k[0]*k[1],k[1],k[2]]
F[25,x,k[0],k[1],k[2]] = F[1,x]+F[26,x,k[0],k[1],k[2]]+F[42,x,k[0],k[1],k[2]]+F[45,x,k[0],k[1],k[2]]+F[48,x,k[0],k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = F[27,x,k[0],k[1],k[2]]*F[7,x]
F[27,x,k[0],k[1],k[2]] = F[28,x,1,k[0],k[1],k[2]]
F[28,x,k[0],k[1],k[2],k[3]] = F[1,x]+F[29,x,k[0],k[1],k[2],k[3]]+F[31,x,k[0],k[1],k[2],k[3]]+F[35,x,k[0],k[1],k[2],k[3]]+F[38,x,k[0],k[1],k[2],k[3]]+F[41,x,k[0],k[1],k[2],k[3]]
F[29,x,k[0],k[1],k[2],k[3]] = F[30,x,k[0],k[1],k[2],k[3]]*F[7,x]
F[30,x,k[0],k[1],k[2],k[3]] = 1/(-1+k[0])*(F[28,x,k[0],k[1],k[2],k[3]]*k[0]-F[28,x,1,k[1],k[2],k[3]])
F[31,x,k[0],k[1],k[2],k[3]] = F[21,x,k[0]]*F[32,x,k[0],k[1],k[2],k[3]]
F[32,x,k[0],k[1],k[2],k[3]] = (F[33,x,k[0],k[1],k[3]]*k[1]-F[33,x,k[0],k[2],k[3]]*k[2])/(-k[2]+k[1])
F[33,x,k[0],k[1],k[2]] = (F[34,x,k[0],1,k[2]]*k[0]-F[34,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[34,x,k[0],k[1],k[2]] = F[25,x,k[0],k[0]*k[1],k[2]]
F[35,x,k[0],k[1],k[2],k[3]] = F[21,x,k[1]]*F[36,x,k[0],k[1],k[2],k[3]]
F[36,x,k[0],k[1],k[2],k[3]] = (-F[37,x,1,k[1],k[2],k[3]]*k[1]+F[37,x,k[0]/k[1],k[1],k[2],k[3]]*k[0])/(-k[1]+k[0])
F[37,x,k[0],k[1],k[2],k[3]] = (F[24,x,k[0],k[1],k[2]]*k[2]-F[24,x,k[0],k[1],k[3]]*k[3])/(-k[3]+k[2])
F[38,x,k[0],k[1],k[2],k[3]] = F[21,x,k[2]]*F[39,x,k[0],k[1],k[2],k[3]]
F[39,x,k[0],k[1],k[2],k[3]] = (F[40,x,k[0],k[1],k[2],1]*k[2]-F[40,x,k[0],k[1],k[2],k[3]/k[2]]*k[3])/(-k[3]+k[2])
F[40,x,k[0],k[1],k[2],k[3]] = F[28,x,k[0],k[1],k[2],k[2]*k[3]]
F[41,x,k[0],k[1],k[2],k[3]] = F[14,x,k[0],k[1],k[2]]*F[21,x,k[3]]
F[42,x,k[0],k[1],k[2]] = F[21,x,k[0]]*F[43,x,k[0],k[1],k[2]]
F[43,x,k[0],k[1],k[2]] = (F[44,x,k[0],k[1]]*k[1]-F[44,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[44,x,k[0],k[1]] = F[24,x,1,k[0],k[1]]
F[45,x,k[0],k[1],k[2]] = F[21,x,k[1]]*F[46,x,k[0],k[1],k[2]]
F[46,x,k[0],k[1],k[2]] = (F[47,x,k[0],k[1],1]*k[1]-F[47,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[47,x,k[0],k[1],k[2]] = F[25,x,k[0],k[1],k[1]*k[2]]
F[48,x,k[0],k[1],k[2]] = F[11,x,k[0],k[1]]*F[21,x,k[2]]
F[49,x,k[0],k[1],k[2]] = F[21,x,k[2]]*F[50,x,k[0],k[1],k[2]]
F[50,x,k[0],k[1],k[2]] = F[40,x,k[0],k[1],k[2],1]
F[51,x,k[0],k[1]] = F[21,x,k[0]]*F[44,x,k[0],k[1]]
F[52,x,k[0],k[1]] = F[21,x,k[1]]*F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = F[47,x,k[0],k[1],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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{6}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y_{0}\right) = \frac{y_{0} F_{4}\! \left(x , y_{0}\right)-F_{4}\! \left(x , 1\right)}{-1+y_{0}}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , 1, y_{0}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{51}\! \left(x , y_{0}, y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , 1, y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{14}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{21}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{19}\! \left(x , y_{0}, y_{1}\right)-y_{2} F_{19}\! \left(x , y_{0}, y_{2}\right)}{-y_{2}+y_{1}}
F_{19}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{20}\! \left(x , y_{0}, 1\right)-y_{1} F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{21}\! \left(x , y_{0}\right) = y_{0} x
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{1}\right) F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-y_{1} F_{24}\! \left(x , 1, y_{1}, y_{2}\right)+y_{0} F_{24}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , 1, y_{0}, y_{1}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{35}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{41}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{30}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{7}\! \left(x \right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{y_{0} F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)-F_{28}\! \left(x , 1, y_{1}, y_{2}, y_{3}\right)}{-1+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{21}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{y_{1} F_{33}\! \left(x , y_{0}, y_{1}, y_{3}\right)-y_{2} F_{33}\! \left(x , y_{0}, y_{2}, y_{3}\right)}{-y_{2}+y_{1}}
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{34}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{34}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{21}\! \left(x , y_{1}\right) F_{36}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{-y_{1} F_{37}\! \left(x , 1, y_{1}, y_{2}, y_{3}\right)+y_{0} F_{37}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}, y_{3}\right)}{-y_{1}+y_{0}}
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{y_{2} F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)-y_{3} F_{24}\! \left(x , y_{0}, y_{1}, y_{3}\right)}{-y_{3}+y_{2}}
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{21}\! \left(x , y_{2}\right) F_{39}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{y_{2} F_{40}\! \left(x , y_{0}, y_{1}, y_{2}, 1\right)-y_{3} F_{40}\! \left(x , y_{0}, y_{1}, y_{2}, \frac{y_{3}}{y_{2}}\right)}{-y_{3}+y_{2}}
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{2} y_{3}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{21}\! \left(x , y_{3}\right)
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{44}\! \left(x , y_{0}, y_{1}\right)-y_{2} F_{44}\! \left(x , y_{0}, y_{2}\right)}{-y_{2}+y_{1}}
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , 1, y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{1}\right) F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{47}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{47}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}, y_{1}\right) F_{21}\! \left(x , y_{2}\right)
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{2}\right) F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{40}\! \left(x , y_{0}, y_{1}, y_{2}, 1\right)
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}\right) F_{44}\! \left(x , y_{0}, y_{1}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{1}\right) F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{47}\! \left(x , y_{0}, y_{1}, 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_7(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0)*F_7(x))
Eq(F_6(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_7(x), x)
Eq(F_8(x, k_0), F_21(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, 1, k_0))
Eq(F_10(x, k_0, k_1), F_11(x, k_0*k_1, k_1))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_51(x, k_0, k_1) + F_52(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_7(x))
Eq(F_13(x, k_0, k_1), F_14(x, 1, k_0, k_1))
Eq(F_14(x, k_0, k_1, k_2), F_1(x) + F_15(x, k_0, k_1, k_2) + F_17(x, k_0, k_1, k_2) + F_22(x, k_0, k_1, k_2) + F_49(x, k_0, k_1, k_2))
Eq(F_15(x, k_0, k_1, k_2), F_16(x, k_0, k_1, k_2)*F_7(x))
Eq(F_16(x, k_0, k_1, k_2), (k_0*F_14(x, k_0, k_1, k_2) - F_14(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_17(x, k_0, k_1, k_2), F_18(x, k_0, k_1, k_2)*F_21(x, k_0))
Eq(F_18(x, k_0, k_1, k_2), (-k_1*F_19(x, k_0, k_1) + k_2*F_19(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_19(x, k_0, k_1), (-k_0*F_20(x, k_0, 1) + k_1*F_20(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1), F_11(x, k_0, k_0*k_1))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0, k_1, k_2), F_21(x, k_1)*F_23(x, k_0, k_1, k_2))
Eq(F_23(x, k_0, k_1, k_2), (-k_0*F_24(x, k_0/k_1, k_1, k_2) + k_1*F_24(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_24(x, k_0, k_1, k_2), F_25(x, k_0*k_1, k_1, k_2))
Eq(F_25(x, k_0, k_1, k_2), F_1(x) + F_26(x, k_0, k_1, k_2) + F_42(x, k_0, k_1, k_2) + F_45(x, k_0, k_1, k_2) + F_48(x, k_0, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), F_27(x, k_0, k_1, k_2)*F_7(x))
Eq(F_27(x, k_0, k_1, k_2), F_28(x, 1, k_0, k_1, k_2))
Eq(F_28(x, k_0, k_1, k_2, k_3), F_1(x) + F_29(x, k_0, k_1, k_2, k_3) + F_31(x, k_0, k_1, k_2, k_3) + F_35(x, k_0, k_1, k_2, k_3) + F_38(x, k_0, k_1, k_2, k_3) + F_41(x, k_0, k_1, k_2, k_3))
Eq(F_29(x, k_0, k_1, k_2, k_3), F_30(x, k_0, k_1, k_2, k_3)*F_7(x))
Eq(F_30(x, k_0, k_1, k_2, k_3), (k_0*F_28(x, k_0, k_1, k_2, k_3) - F_28(x, 1, k_1, k_2, k_3))/(k_0 - 1))
Eq(F_31(x, k_0, k_1, k_2, k_3), F_21(x, k_0)*F_32(x, k_0, k_1, k_2, k_3))
Eq(F_32(x, k_0, k_1, k_2, k_3), (-k_1*F_33(x, k_0, k_1, k_3) + k_2*F_33(x, k_0, k_2, k_3))/(-k_1 + k_2))
Eq(F_33(x, k_0, k_1, k_2), (-k_0*F_34(x, k_0, 1, k_2) + k_1*F_34(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_34(x, k_0, k_1, k_2), F_25(x, k_0, k_0*k_1, k_2))
Eq(F_35(x, k_0, k_1, k_2, k_3), F_21(x, k_1)*F_36(x, k_0, k_1, k_2, k_3))
Eq(F_36(x, k_0, k_1, k_2, k_3), (-k_0*F_37(x, k_0/k_1, k_1, k_2, k_3) + k_1*F_37(x, 1, k_1, k_2, k_3))/(-k_0 + k_1))
Eq(F_37(x, k_0, k_1, k_2, k_3), (-k_2*F_24(x, k_0, k_1, k_2) + k_3*F_24(x, k_0, k_1, k_3))/(-k_2 + k_3))
Eq(F_38(x, k_0, k_1, k_2, k_3), F_21(x, k_2)*F_39(x, k_0, k_1, k_2, k_3))
Eq(F_39(x, k_0, k_1, k_2, k_3), (-k_2*F_40(x, k_0, k_1, k_2, 1) + k_3*F_40(x, k_0, k_1, k_2, k_3/k_2))/(-k_2 + k_3))
Eq(F_40(x, k_0, k_1, k_2, k_3), F_28(x, k_0, k_1, k_2, k_2*k_3))
Eq(F_41(x, k_0, k_1, k_2, k_3), F_14(x, k_0, k_1, k_2)*F_21(x, k_3))
Eq(F_42(x, k_0, k_1, k_2), F_21(x, k_0)*F_43(x, k_0, k_1, k_2))
Eq(F_43(x, k_0, k_1, k_2), (-k_1*F_44(x, k_0, k_1) + k_2*F_44(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_44(x, k_0, k_1), F_24(x, 1, k_0, k_1))
Eq(F_45(x, k_0, k_1, k_2), F_21(x, k_1)*F_46(x, k_0, k_1, k_2))
Eq(F_46(x, k_0, k_1, k_2), (-k_1*F_47(x, k_0, k_1, 1) + k_2*F_47(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_47(x, k_0, k_1, k_2), F_25(x, k_0, k_1, k_1*k_2))
Eq(F_48(x, k_0, k_1, k_2), F_11(x, k_0, k_1)*F_21(x, k_2))
Eq(F_49(x, k_0, k_1, k_2), F_21(x, k_2)*F_50(x, k_0, k_1, k_2))
Eq(F_50(x, k_0, k_1, k_2), F_40(x, k_0, k_1, k_2, 1))
Eq(F_51(x, k_0, k_1), F_21(x, k_0)*F_44(x, k_0, k_1))
Eq(F_52(x, k_0, k_1), F_21(x, k_1)*F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), F_47(x, k_0, k_1, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_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, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "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], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 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