0132_0213_0231_1230
Counting sequence:
1, 1, 2, 6, 20, 69, 242, 857, 3055, 10947, 39406, 142461, 517177, 1885172, 6899012, 25345014, 93455080, 345815601, 1283921603, 4781926878, 17863058431, 66913962465, 251309135714, 946143124941, 3570205942225, 13500599143724, 51153611574827, 194181449554257, 738407997329736, 2812518434007219, 10729058250404726, 40987880829065369, 156798012795657031, 600597301527629931, 2303313674867535210, 8843440167492904089, 33990815546270579737, 130782560008373079772, 503690203973424170333, 1941698254091893401723, 7491782604967082233736, 28930487903538197357535, 111808987987390186089869, 432446479887267525060252, 1673817314288110652676007, 6483209757368146950690669, 25128442165590679125567050, 97459116944864513845215981, 378224327197173552708393505, 1468709360895834660710842812, 5706523877456303386900295651, 22184380921033461385649686281, 86288703582637116107332429192, 335801844144277808797080581091, 1307454892224558406538024118365, 5093042294595026875936614926244, 19848495885363202147840717710247, 77387507318288151103309127347197, 301856534539843554878168057636480, 1177905968686768977525142105468347, 4598276991942024496326323444485681, 17957609779102411920233411058185136, 70156112801697986308725011101183052, 274183319280317938985567878511267382, 1071939403178951153930462429061543832, 4192263011157664240437876323454855489, 16401043436737170106777006866225306635, 64185198975278393223747747411847088166, 251266578506738599334947760919948803263, 983936605898240398485286548758741851473, 3854147816194862690081032903746957679406, 15101320464982238403414034870062368900745, 59186598975155770876839133664560887125329, 232033388945470377892103761192055849350932, 909898776117821001579991657805474690121827, 3569013275929117197570151461030271426099449, 14002733796436611447205785767306466326465320, 54952100884696474136376696690757771732939011, 215704837563664110966964601823823615491377183, 846909496771892482142563847806919234115329918, 3325930472040515869554881963347713183502044871, 13064294965627230219676505032116522278194483545, 51327856117160207816343455409027743525812679764, 201703009906606519282921437119617175510059294167, 792796251882856715887704728457384908980328075617, 3116726370634193296409423745371544793506962544584, 12255234761108751258214432324621243049664887033435, 48197945751097092762539677526226974619690774089721, 189590897718236848525133375103197239160270276483768, 745910442496351279331363340188361858584750207855043, 2935177632783642818894530341708290795801675620147361, 11552045588907866174002783919028781532101378048104040, 45473518712848477785805092181611185939150128550404759, 179032468982736462289573469208312927142032612292906437, 704980452459350869858580006763900552634920141112216602, 2776469406428525306363814153555954246256465056528301869, 10936486151723618770235765840240289973352045395309053505, 43085428713471776372866548883641688002969378981836322396, 169765472724627976243936259619451087042657160758934843123, 669011116295902106090568063051571182296042865975676615833, 2636823373794504294852436621682086746840274052329576352776
Generating function in Maple syntax:
1/2*((x^3-4*x^2+4*x-1)*(1-4*x)^(1/2)-9*x^3+12*x^2-6*x+1)/(x^2-3*x+1)/x^2
Generating function in latex syntax:
\frac{\left(x^{3}-4 x^{2}+4 x -1\right) \sqrt{1-4 x}-9 x^{3}+12 x^{2}-6 x +1}{2 \left(x^{2}-3 x +1\right) x^{2}}
Generating function in sympy syntax:
(-9*x**3/2 + 6*x**2 - 3*x + sqrt(1 - 4*x)*(x**3 - 4*x**2 + 4*x - 1)/2 + 1/2)/(x**2*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
x^2*(x^2-3*x+1)^2*F(x)^2+(3*x-1)*(x^2-3*x+1)*(3*x^2-3*x+1)*F(x)+x^5+12*x^4-28*x^3+23*x^2-8*x+1 = 0
Implicit equation for the generating function in latex syntax:
x^{2} \left(x^{2}-3 x +1\right)^{2} F \! \left(x \right)^{2}+\left(3 x -1\right) \left(x^{2}-3 x +1\right) \left(3 x^{2}-3 x +1\right) F \! \left(x \right)+x^{5}+12 x^{4}-28 x^{3}+23 x^{2}-8 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 69
a(n+6) = -2*(1+2*n)/(8+n)*a(n)-3*(72+25*n)/(8+n)*a(2+n)+(48+29*n)/(8+n)*a(n+1)+(356+85*n)/(8+n)*a(n+3)-3*(82+15*n)/(8+n)*a(n+4)+(74+11*n)/(8+n)*a(n+5), n >= 6
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) = 20
a \! \left(5\right) = 69
a \! \left(n +6\right) = -\frac{2 \left(1+2 n \right) a \! \left(n \right)}{8+n}-\frac{3 \left(72+25 n \right) a \! \left(2+n \right)}{8+n}+\frac{\left(48+29 n \right) a \! \left(n +1\right)}{8+n}+\frac{\left(356+85 n \right) a \! \left(n +3\right)}{8+n}-\frac{3 \left(82+15 n \right) a \! \left(n +4\right)}{8+n}+\frac{\left(74+11 n \right) a \! \left(n +5\right)}{8+n}, \quad n \geq 6
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21166/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[14,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[74,x]
F[4,x] = F[14,x]*F[5,x]
F[5,x] = F[22,x]+F[6,x]
F[6,x] = F[21,x]+F[7,x]
F[7,x] = F[1,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[14,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = x
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[17,x]
F[17,x] = F[14,x]*F[18,x]
F[18,x] = F[1,x]+F[16,x]
F[19,x] = F[20,x]
F[20,x] = F[14,x]*F[15,x]
F[21,x] = F[12,x]
F[22,x] = F[23,x]+F[58,x]
F[23,x] = F[24,x]+F[36,x]
F[24,x] = F[25,x]
F[25,x] = F[14,x]*F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[1,x]+F[14,x]
F[28,x] = F[24,x]+F[29,x]
F[29,x] = F[30,x]+F[31,x]+F[35,x]
F[30,x] = 0
F[31,x] = F[14,x]*F[32,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[14,x]
F[34,x] = F[29,x]
F[35,x] = F[14,x]*F[24,x]
F[36,x] = F[30,x]+F[37,x]+F[41,x]
F[37,x] = F[14,x]*F[38,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[8,x]
F[40,x] = F[36,x]
F[41,x] = F[14,x]*F[42,x]
F[42,x] = F[43,x]+F[48,x]
F[43,x] = F[16,x]+F[44,x]
F[44,x] = F[30,x]+F[45,x]+F[47,x]
F[45,x] = F[14,x]*F[46,x]
F[46,x] = F[12,x]+F[44,x]
F[47,x] = F[14,x]*F[43,x]
F[48,x] = F[49,x]+F[54,x]
F[49,x] = F[30,x]+F[50,x]+F[52,x]
F[50,x] = F[14,x]*F[51,x]
F[51,x] = F[16,x]+F[49,x]
F[52,x] = F[14,x]*F[53,x]
F[53,x] = F[16,x]+F[49,x]
F[54,x] = 2*F[30,x]+F[55,x]+F[57,x]
F[55,x] = F[14,x]*F[56,x]
F[56,x] = F[19,x]+F[54,x]
F[57,x] = F[14,x]*F[48,x]
F[58,x] = F[59,x]
F[59,x] = F[30,x]+F[60,x]+F[72,x]
F[60,x] = F[14,x]*F[61,x]
F[61,x] = F[62,x]+F[65,x]
F[62,x] = F[12,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[12,x]*F[14,x]
F[65,x] = F[59,x]+F[66,x]
F[66,x] = 2*F[30,x]+F[67,x]+F[71,x]
F[67,x] = F[14,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[63,x]
F[70,x] = F[66,x]
F[71,x] = F[14,x]*F[59,x]
F[72,x] = F[14,x]*F[73,x]
F[73,x] = F[24,x]+F[59,x]
F[74,x] = F[14,x]*F[75,x]
F[75,x] = F[76,x,1]
F[76,x,k[0]] = F[1,x]+F[77,x,k[0]]+F[79,x,k[0]]+F[81,x,k[0]]
F[77,x,k[0]] = F[76,x,k[0]]*F[78,x,k[0]]
F[78,x,k[0]] = k[0]*x
F[79,x,k[0]] = F[14,x]*F[80,x,k[0]]
F[80,x,k[0]] = (F[76,x,k[0]]*k[0]-F[76,x,1])/(-1+k[0])
F[81,x,k[0]] = F[14,x]*F[82,x,k[0]]
F[82,x,k[0]] = F[5,x]+F[83,x,k[0]]
F[83,x,k[0]] = F[110,x,k[0]]+F[84,x,k[0]]
F[84,x,k[0]] = F[109,x,k[0]]+F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]+F[89,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[78,x,k[0]]*F[88,x,k[0]]
F[88,x,k[0]] = F[1,x]+F[86,x,k[0]]
F[89,x,k[0]] = F[30,x]+F[90,x,k[0]]+F[92,x,k[0]]
F[90,x,k[0]] = F[78,x,k[0]]*F[91,x,k[0]]
F[91,x,k[0]] = F[8,x]+F[89,x,k[0]]
F[92,x,k[0]] = F[14,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]+F[99,x,k[0]]
F[94,x,k[0]] = F[86,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[30,x]+F[96,x,k[0]]+F[98,x,k[0]]
F[96,x,k[0]] = F[78,x,k[0]]*F[97,x,k[0]]
F[97,x,k[0]] = F[12,x]+F[95,x,k[0]]
F[98,x,k[0]] = F[14,x]*F[94,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[105,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[103,x,k[0]]+F[30,x]
F[101,x,k[0]] = F[102,x,k[0]]*F[78,x,k[0]]
F[102,x,k[0]] = F[100,x,k[0]]+F[16,x]
F[103,x,k[0]] = F[104,x,k[0]]*F[14,x]
F[104,x,k[0]] = F[100,x,k[0]]+F[86,x,k[0]]
F[105,x,k[0]] = 2*F[30,x]+F[106,x,k[0]]+F[108,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[78,x,k[0]]
F[107,x,k[0]] = F[105,x,k[0]]+F[19,x]
F[108,x,k[0]] = F[14,x]*F[99,x,k[0]]
F[109,x,k[0]] = F[95,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[154,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[128,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]+F[117,x,k[0]]+F[30,x]
F[113,x,k[0]] = F[114,x,k[0]]*F[78,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[14,x]
F[115,x,k[0]] = F[113,x,k[0]]+F[116,x,k[0]]+F[30,x]
F[116,x,k[0]] = F[14,x]*F[86,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[14,x]
F[118,x,k[0]] = F[119,x,k[0]]+F[120,x,k[0]]
F[119,x,k[0]] = F[115,x,k[0]]+F[86,x,k[0]]
F[120,x,k[0]] = F[112,x,k[0]]+F[121,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]+F[123,x,k[0]]+F[127,x,k[0]]+F[30,x]
F[122,x,k[0]] = 0
F[123,x,k[0]] = F[124,x,k[0]]*F[14,x]
F[124,x,k[0]] = F[125,x,k[0]]+F[126,x,k[0]]
F[125,x,k[0]] = F[115,x,k[0]]
F[126,x,k[0]] = F[121,x,k[0]]
F[127,x,k[0]] = F[112,x,k[0]]*F[14,x]
F[128,x,k[0]] = F[129,x,k[0]]+F[130,x,k[0]]+F[134,x,k[0]]+F[30,x]
F[129,x,k[0]] = 0
F[130,x,k[0]] = F[131,x,k[0]]*F[14,x]
F[131,x,k[0]] = F[132,x,k[0]]+F[133,x,k[0]]
F[132,x,k[0]] = F[89,x,k[0]]
F[133,x,k[0]] = F[128,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]*F[14,x]
F[135,x,k[0]] = F[136,x,k[0]]+F[144,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]+F[140,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]*F[14,x]
F[139,x,k[0]] = F[137,x,k[0]]+F[86,x,k[0]]
F[140,x,k[0]] = 2*F[30,x]+F[141,x,k[0]]+F[143,x,k[0]]
F[141,x,k[0]] = F[14,x]*F[142,x,k[0]]
F[142,x,k[0]] = F[140,x,k[0]]+F[95,x,k[0]]
F[143,x,k[0]] = F[136,x,k[0]]*F[14,x]
F[144,x,k[0]] = F[145,x,k[0]]+F[150,x,k[0]]
F[145,x,k[0]] = 2*F[30,x]+F[146,x,k[0]]+F[148,x,k[0]]
F[146,x,k[0]] = F[14,x]*F[147,x,k[0]]
F[147,x,k[0]] = F[100,x,k[0]]+F[145,x,k[0]]
F[148,x,k[0]] = F[14,x]*F[149,x,k[0]]
F[149,x,k[0]] = F[137,x,k[0]]+F[145,x,k[0]]
F[150,x,k[0]] = 3*F[30,x]+F[151,x,k[0]]+F[153,x,k[0]]
F[151,x,k[0]] = F[14,x]*F[152,x,k[0]]
F[152,x,k[0]] = F[105,x,k[0]]+F[150,x,k[0]]
F[153,x,k[0]] = F[14,x]*F[144,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]+F[160,x,k[0]]+F[171,x,k[0]]+F[30,x]
F[156,x,k[0]] = F[157,x,k[0]]*F[78,x,k[0]]
F[157,x,k[0]] = F[158,x,k[0]]+F[63,x]
F[158,x,k[0]] = 2*F[30,x]+F[156,x,k[0]]+F[159,x,k[0]]
F[159,x,k[0]] = F[14,x]*F[95,x,k[0]]
F[160,x,k[0]] = F[14,x]*F[161,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]+F[163,x,k[0]]
F[162,x,k[0]] = F[158,x,k[0]]+F[95,x,k[0]]
F[163,x,k[0]] = F[155,x,k[0]]+F[164,x,k[0]]
F[164,x,k[0]] = 2*F[30,x]+F[165,x,k[0]]+F[166,x,k[0]]+F[170,x,k[0]]
F[165,x,k[0]] = 0
F[166,x,k[0]] = F[14,x]*F[167,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]+F[169,x,k[0]]
F[168,x,k[0]] = F[158,x,k[0]]
F[169,x,k[0]] = F[164,x,k[0]]
F[170,x,k[0]] = F[14,x]*F[155,x,k[0]]
F[171,x,k[0]] = F[14,x]*F[172,x,k[0]]
F[172,x,k[0]] = F[112,x,k[0]]+F[155,x,k[0]]
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_{14}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{74}\! \left(x \right)
F_{4}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{22}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{21}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{58}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{36}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{30}\! \left(x \right) = 0
F_{31}\! \left(x \right) = F_{14}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{14}\! \left(x \right)
F_{34}\! \left(x \right) = F_{29}\! \left(x \right)
F_{35}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{8}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{48}\! \left(x \right)
F_{43}\! \left(x \right) = F_{16}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{30}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{14}\! \left(x \right) F_{43}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{54}\! \left(x \right)
F_{49}\! \left(x \right) = F_{30}\! \left(x \right)+F_{50}\! \left(x \right)+F_{52}\! \left(x \right)
F_{50}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{16}\! \left(x \right)+F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{14}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{16}\! \left(x \right)+F_{49}\! \left(x \right)
F_{54}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{14}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right)+F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = F_{14}\! \left(x \right) F_{48}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{30}\! \left(x \right)+F_{60}\! \left(x \right)+F_{72}\! \left(x \right)
F_{60}\! \left(x \right) = F_{14}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{65}\! \left(x \right) = F_{59}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{63}\! \left(x \right)
F_{70}\! \left(x \right) = F_{66}\! \left(x \right)
F_{71}\! \left(x \right) = F_{14}\! \left(x \right) F_{59}\! \left(x \right)
F_{72}\! \left(x \right) = F_{14}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{24}\! \left(x \right)+F_{59}\! \left(x \right)
F_{74}\! \left(x \right) = F_{14}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x , 1\right)
F_{76}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{77}\! \left(x , y\right)+F_{79}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{76}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = y x
F_{79}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = \frac{F_{76}\! \left(x , y\right) y -F_{76}\! \left(x , 1\right)}{-1+y}
F_{81}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{5}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{78}\! \left(x , y\right) F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{86}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{90}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{78}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{8}\! \left(x \right)+F_{89}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{96}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{78}\! \left(x , y\right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{95}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{105}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{103}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{16}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{106}\! \left(x , y\right)+F_{108}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{19}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{95}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{154}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{117}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{14}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{116}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{121}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{123}\! \left(x , y\right)+F_{127}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{122}\! \left(x , y\right) = 0
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{115}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{121}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{130}\! \left(x , y\right)+F_{134}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{129}\! \left(x , y\right) = 0
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{140}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{139}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{141}\! \left(x , y\right)+F_{143}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{14}\! \left(x \right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{146}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{151}\! \left(x , y\right)+F_{153}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{144}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{160}\! \left(x , y\right)+F_{171}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{63}\! \left(x \right)
F_{158}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{156}\! \left(x , y\right)+F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)+F_{163}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{165}\! \left(x , y\right)+F_{166}\! \left(x , y\right)+F_{170}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = 0
F_{166}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{167}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{169}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{158}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{164}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{155}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{14}\! \left(x \right) F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{155}\! \left(x , y\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_14(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_74(x))
Eq(F_4(x), F_14(x)*F_5(x))
Eq(F_5(x), F_22(x) + F_6(x))
Eq(F_6(x), F_21(x) + F_7(x))
Eq(F_7(x), F_1(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_14(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x) + F_19(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_14(x)*F_18(x))
Eq(F_18(x), F_1(x) + F_16(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_14(x)*F_15(x))
Eq(F_21(x), F_12(x))
Eq(F_22(x), F_23(x) + F_58(x))
Eq(F_23(x), F_24(x) + F_36(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_14(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_1(x) + F_14(x))
Eq(F_28(x), F_24(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_31(x) + F_35(x))
Eq(F_30(x), 0)
Eq(F_31(x), F_14(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_14(x))
Eq(F_34(x), F_29(x))
Eq(F_35(x), F_14(x)*F_24(x))
Eq(F_36(x), F_30(x) + F_37(x) + F_41(x))
Eq(F_37(x), F_14(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_8(x))
Eq(F_40(x), F_36(x))
Eq(F_41(x), F_14(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_48(x))
Eq(F_43(x), F_16(x) + F_44(x))
Eq(F_44(x), F_30(x) + F_45(x) + F_47(x))
Eq(F_45(x), F_14(x)*F_46(x))
Eq(F_46(x), F_12(x) + F_44(x))
Eq(F_47(x), F_14(x)*F_43(x))
Eq(F_48(x), F_49(x) + F_54(x))
Eq(F_49(x), F_30(x) + F_50(x) + F_52(x))
Eq(F_50(x), F_14(x)*F_51(x))
Eq(F_51(x), F_16(x) + F_49(x))
Eq(F_52(x), F_14(x)*F_53(x))
Eq(F_53(x), F_16(x) + F_49(x))
Eq(F_54(x), 2*F_30(x) + F_55(x) + F_57(x))
Eq(F_55(x), F_14(x)*F_56(x))
Eq(F_56(x), F_19(x) + F_54(x))
Eq(F_57(x), F_14(x)*F_48(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_30(x) + F_60(x) + F_72(x))
Eq(F_60(x), F_14(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_65(x))
Eq(F_62(x), F_12(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_12(x)*F_14(x))
Eq(F_65(x), F_59(x) + F_66(x))
Eq(F_66(x), 2*F_30(x) + F_67(x) + F_71(x))
Eq(F_67(x), F_14(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_63(x))
Eq(F_70(x), F_66(x))
Eq(F_71(x), F_14(x)*F_59(x))
Eq(F_72(x), F_14(x)*F_73(x))
Eq(F_73(x), F_24(x) + F_59(x))
Eq(F_74(x), F_14(x)*F_75(x))
Eq(F_75(x), F_76(x, 1))
Eq(F_76(x, k_0), F_1(x) + F_77(x, k_0) + F_79(x, k_0) + F_81(x, k_0))
Eq(F_77(x, k_0), F_76(x, k_0)*F_78(x, k_0))
Eq(F_78(x, k_0), k_0*x)
Eq(F_79(x, k_0), F_14(x)*F_80(x, k_0))
Eq(F_80(x, k_0), (-k_0*F_76(x, k_0) + F_76(x, 1))/(1 - k_0))
Eq(F_81(x, k_0), F_14(x)*F_82(x, k_0))
Eq(F_82(x, k_0), F_5(x) + F_83(x, k_0))
Eq(F_83(x, k_0), F_110(x, k_0) + F_84(x, k_0))
Eq(F_84(x, k_0), F_109(x, k_0) + F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0) + F_89(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_78(x, k_0)*F_88(x, k_0))
Eq(F_88(x, k_0), F_1(x) + F_86(x, k_0))
Eq(F_89(x, k_0), F_30(x) + F_90(x, k_0) + F_92(x, k_0))
Eq(F_90(x, k_0), F_78(x, k_0)*F_91(x, k_0))
Eq(F_91(x, k_0), F_8(x) + F_89(x, k_0))
Eq(F_92(x, k_0), F_14(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0) + F_99(x, k_0))
Eq(F_94(x, k_0), F_86(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_30(x) + F_96(x, k_0) + F_98(x, k_0))
Eq(F_96(x, k_0), F_78(x, k_0)*F_97(x, k_0))
Eq(F_97(x, k_0), F_12(x) + F_95(x, k_0))
Eq(F_98(x, k_0), F_14(x)*F_94(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_105(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_103(x, k_0) + F_30(x))
Eq(F_101(x, k_0), F_102(x, k_0)*F_78(x, k_0))
Eq(F_102(x, k_0), F_100(x, k_0) + F_16(x))
Eq(F_103(x, k_0), F_104(x, k_0)*F_14(x))
Eq(F_104(x, k_0), F_100(x, k_0) + F_86(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_108(x, k_0) + 2*F_30(x))
Eq(F_106(x, k_0), F_107(x, k_0)*F_78(x, k_0))
Eq(F_107(x, k_0), F_105(x, k_0) + F_19(x))
Eq(F_108(x, k_0), F_14(x)*F_99(x, k_0))
Eq(F_109(x, k_0), F_95(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_154(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_128(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0) + F_117(x, k_0) + F_30(x))
Eq(F_113(x, k_0), F_114(x, k_0)*F_78(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_14(x))
Eq(F_115(x, k_0), F_113(x, k_0) + F_116(x, k_0) + F_30(x))
Eq(F_116(x, k_0), F_14(x)*F_86(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0)*F_14(x))
Eq(F_118(x, k_0), F_119(x, k_0) + F_120(x, k_0))
Eq(F_119(x, k_0), F_115(x, k_0) + F_86(x, k_0))
Eq(F_120(x, k_0), F_112(x, k_0) + F_121(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_123(x, k_0) + F_127(x, k_0) + F_30(x))
Eq(F_122(x, k_0), 0)
Eq(F_123(x, k_0), F_124(x, k_0)*F_14(x))
Eq(F_124(x, k_0), F_125(x, k_0) + F_126(x, k_0))
Eq(F_125(x, k_0), F_115(x, k_0))
Eq(F_126(x, k_0), F_121(x, k_0))
Eq(F_127(x, k_0), F_112(x, k_0)*F_14(x))
Eq(F_128(x, k_0), F_129(x, k_0) + F_130(x, k_0) + F_134(x, k_0) + F_30(x))
Eq(F_129(x, k_0), 0)
Eq(F_130(x, k_0), F_131(x, k_0)*F_14(x))
Eq(F_131(x, k_0), F_132(x, k_0) + F_133(x, k_0))
Eq(F_132(x, k_0), F_89(x, k_0))
Eq(F_133(x, k_0), F_128(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0)*F_14(x))
Eq(F_135(x, k_0), F_136(x, k_0) + F_144(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0) + F_140(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0)*F_14(x))
Eq(F_139(x, k_0), F_137(x, k_0) + F_86(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0) + F_143(x, k_0) + 2*F_30(x))
Eq(F_141(x, k_0), F_14(x)*F_142(x, k_0))
Eq(F_142(x, k_0), F_140(x, k_0) + F_95(x, k_0))
Eq(F_143(x, k_0), F_136(x, k_0)*F_14(x))
Eq(F_144(x, k_0), F_145(x, k_0) + F_150(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0) + F_148(x, k_0) + 2*F_30(x))
Eq(F_146(x, k_0), F_14(x)*F_147(x, k_0))
Eq(F_147(x, k_0), F_100(x, k_0) + F_145(x, k_0))
Eq(F_148(x, k_0), F_14(x)*F_149(x, k_0))
Eq(F_149(x, k_0), F_137(x, k_0) + F_145(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0) + F_153(x, k_0) + 3*F_30(x))
Eq(F_151(x, k_0), F_14(x)*F_152(x, k_0))
Eq(F_152(x, k_0), F_105(x, k_0) + F_150(x, k_0))
Eq(F_153(x, k_0), F_14(x)*F_144(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0) + F_160(x, k_0) + F_171(x, k_0) + F_30(x))
Eq(F_156(x, k_0), F_157(x, k_0)*F_78(x, k_0))
Eq(F_157(x, k_0), F_158(x, k_0) + F_63(x))
Eq(F_158(x, k_0), F_156(x, k_0) + F_159(x, k_0) + 2*F_30(x))
Eq(F_159(x, k_0), F_14(x)*F_95(x, k_0))
Eq(F_160(x, k_0), F_14(x)*F_161(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0) + F_163(x, k_0))
Eq(F_162(x, k_0), F_158(x, k_0) + F_95(x, k_0))
Eq(F_163(x, k_0), F_155(x, k_0) + F_164(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0) + F_166(x, k_0) + F_170(x, k_0) + 2*F_30(x))
Eq(F_165(x, k_0), 0)
Eq(F_166(x, k_0), F_14(x)*F_167(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0) + F_169(x, k_0))
Eq(F_168(x, k_0), F_158(x, k_0))
Eq(F_169(x, k_0), F_164(x, k_0))
Eq(F_170(x, k_0), F_14(x)*F_155(x, k_0))
Eq(F_171(x, k_0), F_14(x)*F_172(x, k_0))
Eq(F_172(x, k_0), F_112(x, k_0) + F_155(x, k_0))
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": 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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]]}], "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": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "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, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [1, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", 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