0231_1230_3012

Counting sequence:
1, 1, 2, 6, 21, 75, 262, 895, 3022, 10188, 34524, 118030, 407754, 1423886, 5023900, 17895739, 64296859, 232778698, 848432975, 3110718311, 11464777693, 42449136914, 157814199060, 588853096693, 2204397629638, 8276702063359, 31159554480049, 117595344026109, 444801155266050, 1685938292558812, 6402503716674327, 24357382369290593, 92817700357331098, 354244259203323169, 1353953893786911730, 5181975079315781765, 19858301531703971395, 76192514038390136037, 292669033243163304356, 1125404865401494397948, 4331953548765733501079, 16690876685271172341916, 64368583486100510953249, 248455629367452116310647, 959811283219134522607281, 3710806239503586693259198, 14357557458905160499843114, 55591473553007978529906373, 215395970887170552987865016, 835133731173577178435510225, 3240049334104246910888285215, 12578046127753411358361222041, 48857381696332246981530097914, 189885910121127142669081247074, 738399689213519551804716258259, 2872881261283976871868846929730, 11183118690078195028322798428625, 43553133726572206976885692960829, 169699143125473369352751491044399, 661510275841956855514474423791812, 2579785196144158486031077579144746, 10065008424633374238425763343853767, 39284600311290418683131731952864140, 153391884951220826370988327506639238, 599168266992384082031265132173501678, 2341296321604043459904757567842882407, 9152087130484147644824579396190524533, 35787828532746047149830335352305306495, 139990142556996332664025445324050182366, 547774912950351895948519432618360981000, 2144101072479222745605804628701885390631, 8395041335753066889861124994993091878626, 32879946157988923540436551669061803041809, 128814987032095240610626707540485133661271, 504806852806048827055548264175575802413253, 1978810911740277457871939102270260490022878, 7758903456667551479464844623085413841285130, 30430585847086971065260165767856587971642971, 119379905407993296893582502115234346223792454, 468446772357274860576018359449053151549340515, 1838631242459722935404732973452112065039360983, 7218247140337071235991393887089744984426449271, 28344516184440054152356601632737154070380086450, 111327919421401518614825566438111254511308742108, 437355430822333561332216344543071170622368006585, 1718533762922459103887850470345279375914416347072, 6754178532617481550708431721259967465491618967073, 26550689880047910350806667896847224906158268836601, 104391670745385545308208356508077897042193734764505, 410526010156306883200081726457628675040902419085596, 1614724349349419245983664977420864381691146160679248, 6352390004361479018689896162408660340515331467353781, 24995117067004679394580516117192303770111111758427782, 98367296462075987027225323984176671669209072552155989, 387188247672312409642563619513410683935226678086193435, 1524290892786610291810987315799316477108999315820467685, 6001865192663667441874144843790291207375220465931598272, 23636098841064475436083501731772489974417496023248777300, 93096867895752461830372317516905092980426204613529020611, 366743674405086520707437397589509094765416183211802726434, 1444964254224895145597396180991790315904376586693892880451

Generating function in Maple syntax:
(-2*(x-1/2)*(x-1)^4*(1-4*x)^(1/2)-8*x^5+3*x^4+8*x^3-12*x^2+6*x-1)/(12*x^6-38*x^5+52*x^4-38*x^3+14*x^2-2*x)

Generating function in latex syntax:
\frac{-2 \left(x -\frac{1}{2}\right) \left(x -1\right)^{4} \sqrt{1-4 x}-8 x^{5}+3 x^{4}+8 x^{3}-12 x^{2}+6 x -1}{12 x^{6}-38 x^{5}+52 x^{4}-38 x^{3}+14 x^{2}-2 x}

Generating function in sympy syntax:
(-8*x**5 + 3*x**4 + 8*x**3 - 12*x**2 + 6*x + sqrt(1 - 4*x)*(1 - 2*x)*(x - 1)**4 - 1)/(12*x**6 - 38*x**5 + 52*x**4 - 38*x**3 + 14*x**2 - 2*x)

Implicit equation for the generating function in Maple syntax:
x*(x-1)^2*(2*x-1)^2*(3*x^3-5*x^2+4*x-1)^2*F(x)^2+(x-1)*(2*x-1)*(3*x^3-5*x^2+4*x-1)*(8*x^5-3*x^4-8*x^3+12*x^2-6*x+1)*F(x)+4*x^10-21*x^9+142*x^8-410*x^7+678*x^6-719*x^5+511*x^4-243*x^3+74*x^2-13*x+1 = 0

Implicit equation for the generating function in latex syntax:
x \left(x -1\right)^{2} \left(2 x -1\right)^{2} \left(3 x^{3}-5 x^{2}+4 x -1\right)^{2} F \! \left(x \right)^{2}+\left(x -1\right) \left(2 x -1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right) \left(8 x^{5}-3 x^{4}-8 x^{3}+12 x^{2}-6 x +1\right) F \! \left(x \right)+4 x^{10}-21 x^{9}+142 x^{8}-410 x^{7}+678 x^{6}-719 x^{5}+511 x^{4}-243 x^{3}+74 x^{2}-13 x +1 = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 75
a(6) = 262
a(7) = 895
a(n+7) = 24*(1+2*n)/(8+n)*a(n)-4*(88+47*n)/(8+n)*a(1+n)+2*(477+164*n)/(8+n)*a(n+2)-(1268+327*n)/(8+n)*a(n+3)+2*(477+98*n)/(8+n)*a(n+4)-(406+69*n)/(8+n)*a(n+5)+(90+13*n)/(8+n)*a(n+6)+24/(8+n), n >= 8

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) = 21
a \! \left(5\right) = 75
a \! \left(6\right) = 262
a \! \left(7\right) = 895
a \! \left(n +7\right) = \frac{24 \left(1+2 n \right) a \! \left(n \right)}{8+n}-\frac{4 \left(88+47 n \right) a \! \left(1+n \right)}{8+n}+\frac{2 \left(477+164 n \right) a \! \left(n +2\right)}{8+n}-\frac{\left(1268+327 n \right) a \! \left(n +3\right)}{8+n}+\frac{2 \left(477+98 n \right) a \! \left(n +4\right)}{8+n}-\frac{\left(406+69 n \right) a \! \left(n +5\right)}{8+n}+\frac{\left(90+13 n \right) a \! \left(n +6\right)}{8+n}+\frac{24}{8+n}, \quad n \geq 8

Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/368/
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[5,x]
F[3,x] = F[1,x]+F[4,x]+F[93,x]
F[4,x] = F[5,x]*F[7,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = k[0]*x
F[7,x] = F[1,x]+F[8,x]+F[85,x]+F[92,x]
F[8,x] = F[5,x]*F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[69,x,k[0]]+F[71,x,k[0]]+F[79,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[5,x]
F[12,x,k[0]] = F[13,x,k[0]]+F[34,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]+F[24,x,k[0]]
F[14,x,k[0]] = F[15,x]+F[18,x,k[0]]
F[15,x] = F[1,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[5,x]
F[18,x,k[0]] = F[19,x,k[0]]+F[22,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[6,x,k[0]]
F[21,x,k[0]] = F[1,x]+F[19,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[18,x,k[0]]*F[5,x]
F[24,x,k[0]] = F[25,x]+F[28,x,k[0]]
F[25,x] = F[16,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[25,x]*F[5,x]
F[28,x,k[0]] = F[29,x,k[0]]+F[32,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]*F[6,x,k[0]]
F[31,x,k[0]] = F[16,x]+F[29,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[28,x,k[0]]*F[5,x]
F[34,x,k[0]] = F[35,x,k[0]]+F[50,x,k[0]]
F[35,x,k[0]] = F[36,x]+F[40,x,k[0]]
F[36,x] = F[16,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[5,x]
F[39,x] = F[16,x]+F[37,x]
F[40,x,k[0]] = F[41,x,k[0]]+F[47,x,k[0]]
F[41,x,k[0]] = F[42,x]+F[43,x,k[0]]+F[45,x,k[0]]
F[42,x] = 0
F[43,x,k[0]] = F[44,x,k[0]]*F[5,x]
F[44,x,k[0]] = F[19,x,k[0]]+F[41,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]*F[6,x,k[0]]
F[46,x,k[0]] = F[16,x]+F[41,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]*F[5,x]
F[49,x,k[0]] = F[22,x,k[0]]+F[47,x,k[0]]
F[50,x,k[0]] = F[51,x]+F[60,x,k[0]]
F[51,x] = F[52,x]+F[57,x]
F[52,x] = F[42,x]+F[53,x]+F[55,x]
F[53,x] = F[5,x]*F[54,x]
F[54,x] = F[16,x]+F[52,x]
F[55,x] = F[5,x]*F[56,x]
F[56,x] = F[16,x]+F[52,x]
F[57,x] = F[58,x]
F[58,x] = F[5,x]*F[59,x]
F[59,x] = F[26,x]+F[57,x]
F[60,x,k[0]] = F[61,x,k[0]]+F[66,x,k[0]]
F[61,x,k[0]] = 2*F[42,x]+F[62,x,k[0]]+F[64,x,k[0]]
F[62,x,k[0]] = F[5,x]*F[63,x,k[0]]
F[63,x,k[0]] = F[29,x,k[0]]+F[61,x,k[0]]
F[64,x,k[0]] = F[6,x,k[0]]*F[65,x,k[0]]
F[65,x,k[0]] = F[52,x]+F[61,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[5,x]*F[68,x,k[0]]
F[68,x,k[0]] = F[32,x,k[0]]+F[66,x,k[0]]
F[69,x,k[0]] = F[5,x]*F[70,x,k[0]]
F[70,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[71,x,k[0]] = F[6,x,k[0]]*F[72,x,k[0]]
F[72,x,k[0]] = F[1,x]+F[71,x,k[0]]+F[73,x,k[0]]+F[77,x,k[0]]
F[73,x,k[0]] = F[5,x]*F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]+F[76,x,k[0]]
F[75,x,k[0]] = F[21,x,k[0]]+F[31,x,k[0]]
F[76,x,k[0]] = F[46,x,k[0]]+F[65,x,k[0]]
F[77,x,k[0]] = F[5,x]*F[78,x,k[0]]
F[78,x,k[0]] = 1/(-1+k[0])*(F[72,x,k[0]]*k[0]-F[72,x,1])
F[79,x,k[0]] = F[5,x]*F[80,x,k[0]]
F[80,x,k[0]] = F[14,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[56,x]+F[82,x,k[0]]
F[82,x,k[0]] = F[29,x,k[0]]+F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[5,x]*F[82,x,k[0]]
F[85,x] = F[5,x]*F[86,x]
F[86,x] = 2*F[85,x]+F[1,x]+F[8,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[15,x]*F[5,x]*F[89,x]
F[89,x] = F[1,x]+F[90,x]+F[92,x]
F[90,x] = F[91,x,1]
F[91,x,k[0]] = F[5,x]*F[72,x,k[0]]
F[92,x] = F[5,x]*F[7,x]
F[93,x] = F[5,x]*F[94,x]
F[94,x] = F[72,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_{5}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{93}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{7}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = y x
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{8}\! \left(x \right)+F_{85}\! \left(x \right)+F_{92}\! \left(x \right)
F_{8}\! \left(x \right) = F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{69}\! \left(x , y\right)+F_{71}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{5}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{28}\! \left(x , y\right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{25}\! \left(x \right) F_{5}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x \right)+F_{40}\! \left(x , y\right)
F_{36}\! \left(x \right) = F_{16}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{5}\! \left(x \right)
F_{39}\! \left(x \right) = F_{16}\! \left(x \right)+F_{37}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{42}\! \left(x \right) = 0
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{44}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{41}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x \right)+F_{60}\! \left(x , y\right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{57}\! \left(x \right)
F_{52}\! \left(x \right) = F_{42}\! \left(x \right)+F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = F_{5}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{16}\! \left(x \right)+F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{5}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{16}\! \left(x \right)+F_{52}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{5}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{26}\! \left(x \right)+F_{57}\! \left(x \right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = 2 F_{42}\! \left(x \right)+F_{62}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{52}\! \left(x \right)+F_{61}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = -\frac{-y F_{10}\! \left(x , y\right)+F_{10}\! \left(x , 1\right)}{-1+y}
F_{71}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{71}\! \left(x , y\right)+F_{73}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{46}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = -\frac{-y F_{72}\! \left(x , y\right)+F_{72}\! \left(x , 1\right)}{-1+y}
F_{79}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{56}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{85}\! \left(x \right) = F_{5}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{85}\! \left(x \right)+F_{1}\! \left(x \right)+F_{8}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{15}\! \left(x \right) F_{5}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{1}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x , 1\right)
F_{91}\! \left(x , y\right) = F_{5}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{92}\! \left(x \right) = F_{5}\! \left(x \right) F_{7}\! \left(x \right)
F_{93}\! \left(x \right) = F_{5}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{72}\! \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_5(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_93(x))
Eq(F_4(x), F_5(x)*F_7(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), k_0*x)
Eq(F_7(x), F_1(x) + F_8(x) + F_85(x) + F_92(x))
Eq(F_8(x), F_5(x)*F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0) + F_69(x, k_0) + F_71(x, k_0) + F_79(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_5(x))
Eq(F_12(x, k_0), F_13(x, k_0) + F_34(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0) + F_24(x, k_0))
Eq(F_14(x, k_0), F_15(x) + F_18(x, k_0))
Eq(F_15(x), F_1(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_5(x))
Eq(F_18(x, k_0), F_19(x, k_0) + F_22(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_6(x, k_0))
Eq(F_21(x, k_0), F_1(x) + F_19(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_18(x, k_0)*F_5(x))
Eq(F_24(x, k_0), F_25(x) + F_28(x, k_0))
Eq(F_25(x), F_16(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_25(x)*F_5(x))
Eq(F_28(x, k_0), F_29(x, k_0) + F_32(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0)*F_6(x, k_0))
Eq(F_31(x, k_0), F_16(x) + F_29(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_28(x, k_0)*F_5(x))
Eq(F_34(x, k_0), F_35(x, k_0) + F_50(x, k_0))
Eq(F_35(x, k_0), F_36(x) + F_40(x, k_0))
Eq(F_36(x), F_16(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_5(x))
Eq(F_39(x), F_16(x) + F_37(x))
Eq(F_40(x, k_0), F_41(x, k_0) + F_47(x, k_0))
Eq(F_41(x, k_0), F_42(x) + F_43(x, k_0) + F_45(x, k_0))
Eq(F_42(x), 0)
Eq(F_43(x, k_0), F_44(x, k_0)*F_5(x))
Eq(F_44(x, k_0), F_19(x, k_0) + F_41(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0)*F_6(x, k_0))
Eq(F_46(x, k_0), F_16(x) + F_41(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0)*F_5(x))
Eq(F_49(x, k_0), F_22(x, k_0) + F_47(x, k_0))
Eq(F_50(x, k_0), F_51(x) + F_60(x, k_0))
Eq(F_51(x), F_52(x) + F_57(x))
Eq(F_52(x), F_42(x) + F_53(x) + F_55(x))
Eq(F_53(x), F_5(x)*F_54(x))
Eq(F_54(x), F_16(x) + F_52(x))
Eq(F_55(x), F_5(x)*F_56(x))
Eq(F_56(x), F_16(x) + F_52(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_5(x)*F_59(x))
Eq(F_59(x), F_26(x) + F_57(x))
Eq(F_60(x, k_0), F_61(x, k_0) + F_66(x, k_0))
Eq(F_61(x, k_0), 2*F_42(x) + F_62(x, k_0) + F_64(x, k_0))
Eq(F_62(x, k_0), F_5(x)*F_63(x, k_0))
Eq(F_63(x, k_0), F_29(x, k_0) + F_61(x, k_0))
Eq(F_64(x, k_0), F_6(x, k_0)*F_65(x, k_0))
Eq(F_65(x, k_0), F_52(x) + F_61(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_5(x)*F_68(x, k_0))
Eq(F_68(x, k_0), F_32(x, k_0) + F_66(x, k_0))
Eq(F_69(x, k_0), F_5(x)*F_70(x, k_0))
Eq(F_70(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_71(x, k_0), F_6(x, k_0)*F_72(x, k_0))
Eq(F_72(x, k_0), F_1(x) + F_71(x, k_0) + F_73(x, k_0) + F_77(x, k_0))
Eq(F_73(x, k_0), F_5(x)*F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0) + F_76(x, k_0))
Eq(F_75(x, k_0), F_21(x, k_0) + F_31(x, k_0))
Eq(F_76(x, k_0), F_46(x, k_0) + F_65(x, k_0))
Eq(F_77(x, k_0), F_5(x)*F_78(x, k_0))
Eq(F_78(x, k_0), (k_0*F_72(x, k_0) - F_72(x, 1))/(k_0 - 1))
Eq(F_79(x, k_0), F_5(x)*F_80(x, k_0))
Eq(F_80(x, k_0), F_14(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_56(x) + F_82(x, k_0))
Eq(F_82(x, k_0), F_29(x, k_0) + F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_5(x)*F_82(x, k_0))
Eq(F_85(x), F_5(x)*F_86(x))
Eq(F_86(x), F_1(x) + F_8(x) + 2*F_85(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_15(x)*F_5(x)*F_89(x))
Eq(F_89(x), F_1(x) + F_90(x) + F_92(x))
Eq(F_90(x), F_91(x, 1))
Eq(F_91(x, k_0), F_5(x)*F_72(x, k_0))
Eq(F_92(x), F_5(x)*F_7(x))
Eq(F_93(x), F_5(x)*F_94(x))
Eq(F_94(x), F_72(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": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[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], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[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]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": 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