0123_0132_1230_3012
Counting sequence:
1, 1, 2, 6, 20, 67, 217, 687, 2176, 7018, 23223, 78827, 273367, 964029, 3443355, 12420757, 45154368, 165204284, 607684131, 2245698617, 8332970435, 31033551743, 115955146423, 434554791548, 1632988966699, 6151900930626, 23229400199401, 87901105391821, 333281905413765, 1265990973822353, 4817230329493951, 18359625762709137, 70078707358921440, 267870208174423984, 1025280198332048763, 3929229588596956437, 15076083983847338411, 57910602916641052819, 222684667523945796239, 857159235341616787716, 3302552415655735997399, 12736045637212925863222, 49158348510139412697337, 189897909130183936101657, 734153598824470324886189, 2840417973723021325680549, 10997446565715974580919991, 42609102468935326510524314, 165196671999782624831180075, 640880143422630928464618496, 2487813902937466641540743621, 9663047328273854738577444115, 37553952616293697734816863565, 146027038401568570999581218327, 568117589483762927295930713067, 2211374334636826385635621280846, 8611871544453800454933199021145, 33553409784619941574576997315378, 130789413145897588283307771840253, 510033455416700154455270222284817, 1989795959723698757799673138100161, 7765978923180979151938367452705593, 30321865701630489393727567041000839, 118435588301817620448704898781802313, 462775020434588666937060538231833248, 1808897743026736383691731158094279128, 7073100157711232514546870042359206955, 27666406606516830419713397204430319693, 108252649020916803632266051046797666619, 423704426509176262168413149656829392123, 1658907610930498247817613401721417167807, 6496992033066387833450657233337542128932, 25452460314355505429431488486554188489311, 99740379754786777718304335649212860504094, 390960367676180699007078728048376290232377, 1532892532741482133022965411321207024568849, 6011804584793682723270483725991698095343005, 23583551657173188486766421078660152644210701, 92538386338342343035354860316090360394129383, 363195324786797357914880692248849068407209654, 1425809659122601171387730111763580167718016887, 5598649627935656754398500951969644527716916920, 21988875065605097317205635370339476594971316125, 86381026148396971542637699662419678329506850115, 339411892172175312736559529543507964663880204437, 1333911153961668954001737149771986527344193276927, 5243433776478798570487848543093066921552661228299, 20615394908221951531584072902691159610597922131342, 81068575420428341167566246674423799623652251885793, 318857418889763710894451006720017292584435123016922, 1254358759104355578453354548225442439519420854487421, 4935446834384359467347256537120009230277317513721961, 19422670056075894092546187964181928454069612251647825, 76448234357832305158590905399888463548546958876597153, 300954222053417420920378369914867314747377154029397111, 1184967143495505213021521706499538205541764780938889478, 4666417002383382593416476530676430027943243845990495819, 18379372560535529822580748625720766964215474428974589580, 72401287425730933219204578930068864181319712136987817277, 285252188863830707444007241954469660461234465348896418863, 1124028777884360846348989612371265386719223306385416880541
Generating function in Maple syntax:
1/2*(-2*(x+1)*(x-1)^6*(x-1/2)*(1-4*x)^(1/2)+8*x^8-37*x^7+81*x^6-83*x^5+35*x^4+9*x^3-17*x^2+7*x-1)/x/(2*x-1)/(x-1)^6
Generating function in latex syntax:
\frac{-2 \left(x +1\right) \left(x -1\right)^{6} \left(x -\frac{1}{2}\right) \sqrt{1-4 x}+8 x^{8}-37 x^{7}+81 x^{6}-83 x^{5}+35 x^{4}+9 x^{3}-17 x^{2}+7 x -1}{2 x \left(2 x -1\right) \left(x -1\right)^{6}}
Generating function in sympy syntax:
(4*x**8 - 37*x**7/2 + 81*x**6/2 - 83*x**5/2 + 35*x**4/2 + 9*x**3/2 - 17*x**2/2 + 7*x/2 + sqrt(1 - 4*x)*(-2*x - 2)*(x - 1)**6*(x - 1/2)/2 - 1/2)/(x*(x - 1)**6*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x-1)^12*F(x)^2-(2*x-1)*(8*x^8-37*x^7+81*x^6-83*x^5+35*x^4+9*x^3-17*x^2+7*x-1)*(x-1)^6*F(x)+4*x^16-29*x^15+76*x^14+31*x^13-758*x^12+2412*x^11-4256*x^10+4712*x^9-3050*x^8+417*x^7+1363*x^6-1616*x^5+1007*x^4-399*x^3+101*x^2-15*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x -1\right)^{12} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(8 x^{8}-37 x^{7}+81 x^{6}-83 x^{5}+35 x^{4}+9 x^{3}-17 x^{2}+7 x -1\right) \left(x -1\right)^{6} F \! \left(x \right)+4 x^{16}-29 x^{15}+76 x^{14}+31 x^{13}-758 x^{12}+2412 x^{11}-4256 x^{10}+4712 x^{9}-3050 x^{8}+417 x^{7}+1363 x^{6}-1616 x^{5}+1007 x^{4}-399 x^{3}+101 x^{2}-15 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 67
a(6) = 217
a(7) = 687
a(8) = 2176
a(9) = 7018
a(10) = 23223
a(11) = 78827
a(n+4) = 8*(2*n-1)/(n+5)*a(n)-4*(n-3)/(n+5)*a(1+n)-2*(6*n+19)/(n+5)*a(n+2)+(7*n+27)/(n+5)*a(n+3)-1/120*(6*n^6-127*n^5+585*n^4-435*n^3+2649*n^2-3158*n+720)/(n+5), n >= 12
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) = 67
a \! \left(6\right) = 217
a \! \left(7\right) = 687
a \! \left(8\right) = 2176
a \! \left(9\right) = 7018
a \! \left(10\right) = 23223
a \! \left(11\right) = 78827
a \! \left(n +4\right) = \frac{8 \left(2 n -1\right) a \! \left(n \right)}{n +5}-\frac{4 \left(n -3\right) a \! \left(1+n \right)}{n +5}-\frac{2 \left(6 n +19\right) a \! \left(n +2\right)}{n +5}+\frac{\left(7 n +27\right) a \! \left(n +3\right)}{n +5}-\frac{6 n^{6}-127 n^{5}+585 n^{4}-435 n^{3}+2649 n^{2}-3158 n +720}{120 \left(n +5\right)}, \quad n \geq 12
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21141/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[16,x]*F[3,x]
F[3,x] = F[1,x]+F[172,x]+F[4,x]
F[4,x] = F[16,x]*F[5,x]
F[5,x] = F[1,x]+F[123,x]+F[6,x]+F[85,x]
F[6,x] = F[16,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[1,x]+F[69,x,k[0]]+F[71,x,k[0]]+F[79,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[16,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[34,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]+F[24,x,k[0]]
F[12,x,k[0]] = F[13,x]+F[17,x,k[0]]
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]
F[16,x] = x
F[17,x,k[0]] = F[18,x,k[0]]+F[22,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[21,x,k[0]]
F[20,x,k[0]] = F[1,x]+F[18,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[16,x]*F[17,x,k[0]]
F[24,x,k[0]] = F[25,x]+F[28,x,k[0]]
F[25,x] = F[14,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[16,x]*F[25,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[21,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = F[14,x]+F[29,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[16,x]*F[28,x,k[0]]
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[14,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[16,x]*F[39,x]
F[39,x] = F[14,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[16,x]*F[44,x,k[0]]
F[44,x,k[0]] = F[18,x,k[0]]+F[41,x,k[0]]
F[45,x,k[0]] = F[21,x,k[0]]*F[46,x,k[0]]
F[46,x,k[0]] = F[14,x]+F[41,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[16,x]*F[49,x,k[0]]
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[16,x]*F[54,x]
F[54,x] = F[14,x]+F[52,x]
F[55,x] = F[16,x]*F[56,x]
F[56,x] = F[14,x]+F[52,x]
F[57,x] = F[58,x]
F[58,x] = F[16,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[16,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[21,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[16,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[16,x]*F[70,x,k[0]]
F[70,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[71,x,k[0]] = F[21,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[16,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[20,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[16,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[16,x]*F[80,x,k[0]]
F[80,x,k[0]] = F[12,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[16,x]*F[82,x,k[0]]
F[85,x] = F[16,x]*F[86,x]
F[86,x] = F[114,x]+F[87,x]
F[87,x] = F[100,x]+F[88,x]
F[88,x] = F[1,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[16,x]*F[91,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = F[1,x]+F[16,x]
F[93,x] = F[89,x]+F[94,x]
F[94,x] = F[42,x]+F[95,x]+F[99,x]
F[95,x] = F[16,x]*F[96,x]
F[96,x] = F[97,x]+F[98,x]
F[97,x] = F[16,x]
F[98,x] = F[94,x]
F[99,x] = F[16,x]*F[89,x]
F[100,x] = F[101,x]+F[14,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[16,x]
F[103,x] = F[104,x]+F[107,x]
F[104,x] = F[105,x]+F[14,x]
F[105,x] = F[106,x]
F[106,x] = F[14,x]*F[16,x]
F[107,x] = F[101,x]+F[108,x]
F[108,x] = 2*F[42,x]+F[109,x]+F[113,x]
F[109,x] = F[110,x]*F[16,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[105,x]
F[112,x] = F[108,x]
F[113,x] = F[101,x]*F[16,x]
F[114,x] = F[115,x]+F[119,x]
F[115,x] = F[116,x]+F[14,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[16,x]
F[118,x] = F[116,x]+F[89,x]
F[119,x] = F[120,x]+F[52,x]
F[120,x] = F[121,x]
F[121,x] = F[122,x]*F[16,x]
F[122,x] = F[101,x]+F[120,x]
F[123,x] = F[124,x]*F[16,x]
F[124,x] = F[125,x]+F[87,x]
F[125,x] = F[126,x]+F[161,x]
F[126,x] = F[127,x]+F[14,x]
F[127,x] = F[128,x]+F[130,x]+F[42,x]
F[128,x] = F[129,x]*F[16,x]
F[129,x] = F[127,x]+F[89,x]
F[130,x] = F[131,x]*F[16,x]
F[131,x] = F[132,x]+F[136,x]
F[132,x] = F[133,x]+F[14,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[16,x]
F[135,x] = F[133,x]+F[16,x]
F[136,x] = F[137,x]+F[149,x]
F[137,x] = F[138,x]+F[42,x]+F[53,x]
F[138,x] = F[139,x]*F[16,x]
F[139,x] = F[132,x]+F[140,x]
F[140,x] = F[137,x]+F[141,x]
F[141,x] = 2*F[42,x]+F[142,x]+F[145,x]
F[142,x] = F[143,x]*F[16,x]
F[143,x] = F[105,x]+F[144,x]
F[144,x] = F[142,x]
F[145,x] = F[146,x]*F[16,x]
F[146,x] = F[147,x]+F[148,x]
F[147,x] = F[133,x]
F[148,x] = F[141,x]
F[149,x] = 2*F[42,x]+F[150,x]+F[158,x]
F[150,x] = F[151,x]*F[16,x]
F[151,x] = F[152,x]+F[155,x]
F[152,x] = F[106,x]+F[153,x]+F[42,x]
F[153,x] = F[154,x]*F[16,x]
F[154,x] = F[152,x]+F[16,x]
F[155,x] = 2*F[42,x]+F[150,x]+F[156,x]
F[156,x] = F[157,x]*F[16,x]
F[157,x] = F[133,x]+F[155,x]
F[158,x] = F[159,x]*F[16,x]
F[159,x] = F[147,x]+F[160,x]
F[160,x] = F[149,x]
F[161,x] = F[162,x]+F[52,x]
F[162,x] = 2*F[42,x]+F[163,x]+F[165,x]
F[163,x] = F[16,x]*F[164,x]
F[164,x] = F[101,x]+F[162,x]
F[165,x] = F[16,x]*F[166,x]
F[166,x] = F[167,x]+F[168,x]
F[167,x] = F[26,x]
F[168,x] = F[169,x]
F[169,x] = F[16,x]*F[170,x]
F[170,x] = F[167,x]+F[171,x]
F[171,x] = F[169,x]
F[172,x] = F[16,x]*F[173,x]
F[173,x] = F[1,x]+F[174,x]+F[196,x]+F[230,x]
F[174,x] = F[16,x]*F[175,x]
F[175,x] = F[176,x]+F[180,x]
F[176,x] = F[13,x]+F[177,x]
F[177,x] = F[14,x]+F[178,x]
F[178,x] = F[153,x]+F[179,x]+F[42,x]
F[179,x] = F[16,x]*F[177,x]
F[180,x] = F[181,x]+F[56,x]
F[181,x] = F[182,x]+F[52,x]
F[182,x] = F[156,x]+F[183,x]+F[185,x]+F[42,x]
F[183,x] = F[16,x]*F[184,x]
F[184,x] = F[178,x]+F[182,x]
F[185,x] = F[16,x]*F[186,x]
F[186,x] = F[187,x]+F[52,x]
F[187,x] = F[185,x]+F[188,x]+F[193,x]+F[42,x]
F[188,x] = F[16,x]*F[189,x]
F[189,x] = F[190,x]+F[26,x]
F[190,x] = 2*F[42,x]+F[188,x]+F[191,x]
F[191,x] = F[16,x]*F[192,x]
F[192,x] = F[190,x]+F[52,x]
F[193,x] = F[16,x]*F[194,x]
F[194,x] = F[133,x]+F[195,x]
F[195,x] = 2*F[42,x]+F[142,x]+F[193,x]
F[196,x] = F[16,x]*F[197,x]
F[197,x] = F[198,x,1]
F[198,x,k[0]] = F[1,x]+F[199,x,k[0]]+F[226,x,k[0]]+F[228,x,k[0]]+F[71,x,k[0]]
F[199,x,k[0]] = F[16,x]*F[200,x,k[0]]
F[200,x,k[0]] = F[201,x,k[0]]+F[206,x,k[0]]
F[201,x,k[0]] = F[12,x,k[0]]+F[202,x,k[0]]
F[202,x,k[0]] = F[177,x]+F[203,x,k[0]]
F[203,x,k[0]] = F[204,x,k[0]]+F[29,x,k[0]]
F[204,x,k[0]] = F[205,x,k[0]]
F[205,x,k[0]] = F[16,x]*F[203,x,k[0]]
F[206,x,k[0]] = F[207,x,k[0]]+F[213,x,k[0]]
F[207,x,k[0]] = F[208,x,k[0]]+F[56,x]
F[208,x,k[0]] = F[209,x,k[0]]+F[41,x,k[0]]
F[209,x,k[0]] = 2*F[42,x]+F[210,x,k[0]]+F[212,x,k[0]]
F[210,x,k[0]] = F[16,x]*F[211,x,k[0]]
F[211,x,k[0]] = F[209,x,k[0]]+F[22,x,k[0]]
F[212,x,k[0]] = F[16,x]*F[208,x,k[0]]
F[213,x,k[0]] = F[181,x]+F[214,x,k[0]]
F[214,x,k[0]] = F[215,x,k[0]]+F[61,x,k[0]]
F[215,x,k[0]] = 3*F[42,x]+F[216,x,k[0]]+F[218,x,k[0]]
F[216,x,k[0]] = F[16,x]*F[217,x,k[0]]
F[217,x,k[0]] = F[204,x,k[0]]+F[215,x,k[0]]
F[218,x,k[0]] = F[16,x]*F[219,x,k[0]]
F[219,x,k[0]] = F[220,x,k[0]]+F[61,x,k[0]]
F[220,x,k[0]] = 3*F[42,x]+F[218,x,k[0]]+F[221,x,k[0]]
F[221,x,k[0]] = F[16,x]*F[222,x,k[0]]
F[222,x,k[0]] = F[223,x,k[0]]+F[32,x,k[0]]
F[223,x,k[0]] = 3*F[42,x]+F[221,x,k[0]]+F[224,x,k[0]]
F[224,x,k[0]] = F[16,x]*F[225,x,k[0]]
F[225,x,k[0]] = F[223,x,k[0]]+F[61,x,k[0]]
F[226,x,k[0]] = F[16,x]*F[227,x,k[0]]
F[227,x,k[0]] = 1/(-1+k[0])*(F[198,x,k[0]]*k[0]-F[198,x,1])
F[228,x,k[0]] = F[16,x]*F[229,x,k[0]]
F[229,x,k[0]] = 1/(-1+k[0])*(F[72,x,k[0]]*k[0]-F[72,x,1])
F[230,x] = F[71,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_{16}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{172}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{123}\! \left(x \right)+F_{6}\! \left(x \right)+F_{85}\! \left(x \right)
F_{6}\! \left(x \right) = F_{16}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{69}\! \left(x , y\right)+F_{71}\! \left(x , y\right)+F_{79}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{16}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{17}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{28}\! \left(x , y\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_{27}\! \left(x \right) = F_{16}\! \left(x \right) F_{25}\! \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_{21}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{14}\! \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_{16}\! \left(x \right) F_{28}\! \left(x , y\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_{14}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{14}\! \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_{16}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{14}\! \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_{16}\! \left(x \right) F_{49}\! \left(x , y\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_{16}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{14}\! \left(x \right)+F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{16}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{14}\! \left(x \right)+F_{52}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{16}\! \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_{16}\! \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_{21}\! \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_{16}\! \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_{16}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{71}\! \left(x , y\right) = F_{21}\! \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_{16}\! \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_{20}\! \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_{16}\! \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_{16}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{12}\! \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_{16}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{85}\! \left(x \right) = F_{16}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{114}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{100}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{1}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{16}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{92}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{93}\! \left(x \right) = F_{89}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{42}\! \left(x \right)+F_{95}\! \left(x \right)+F_{99}\! \left(x \right)
F_{95}\! \left(x \right) = F_{16}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{98}\! \left(x \right)
F_{97}\! \left(x \right) = F_{16}\! \left(x \right)
F_{98}\! \left(x \right) = F_{94}\! \left(x \right)
F_{99}\! \left(x \right) = F_{16}\! \left(x \right) F_{89}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{14}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{16}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{107}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{14}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{107}\! \left(x \right) = F_{101}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = 2 F_{42}\! \left(x \right)+F_{109}\! \left(x \right)+F_{113}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{16}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{105}\! \left(x \right)
F_{112}\! \left(x \right) = F_{108}\! \left(x \right)
F_{113}\! \left(x \right) = F_{101}\! \left(x \right) F_{16}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{119}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{14}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{16}\! \left(x \right)
F_{118}\! \left(x \right) = F_{116}\! \left(x \right)+F_{89}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{52}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{16}\! \left(x \right)
F_{122}\! \left(x \right) = F_{101}\! \left(x \right)+F_{120}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{16}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{87}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{161}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{14}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{130}\! \left(x \right)+F_{42}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{16}\! \left(x \right)
F_{129}\! \left(x \right) = F_{127}\! \left(x \right)+F_{89}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{16}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{136}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{14}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{16}\! \left(x \right)
F_{135}\! \left(x \right) = F_{133}\! \left(x \right)+F_{16}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{149}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{42}\! \left(x \right)+F_{53}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{16}\! \left(x \right)
F_{139}\! \left(x \right) = F_{132}\! \left(x \right)+F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{137}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = 2 F_{42}\! \left(x \right)+F_{142}\! \left(x \right)+F_{145}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{16}\! \left(x \right)
F_{143}\! \left(x \right) = F_{105}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{142}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{16}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{148}\! \left(x \right)
F_{147}\! \left(x \right) = F_{133}\! \left(x \right)
F_{148}\! \left(x \right) = F_{141}\! \left(x \right)
F_{149}\! \left(x \right) = 2 F_{42}\! \left(x \right)+F_{150}\! \left(x \right)+F_{158}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right) F_{16}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{155}\! \left(x \right)
F_{152}\! \left(x \right) = F_{106}\! \left(x \right)+F_{153}\! \left(x \right)+F_{42}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{16}\! \left(x \right)
F_{154}\! \left(x \right) = F_{152}\! \left(x \right)+F_{16}\! \left(x \right)
F_{155}\! \left(x \right) = 2 F_{42}\! \left(x \right)+F_{150}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right) F_{16}\! \left(x \right)
F_{157}\! \left(x \right) = F_{133}\! \left(x \right)+F_{155}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{16}\! \left(x \right)
F_{159}\! \left(x \right) = F_{147}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{149}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{52}\! \left(x \right)
F_{162}\! \left(x \right) = 2 F_{42}\! \left(x \right)+F_{163}\! \left(x \right)+F_{165}\! \left(x \right)
F_{163}\! \left(x \right) = F_{16}\! \left(x \right) F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{101}\! \left(x \right)+F_{162}\! \left(x \right)
F_{165}\! \left(x \right) = F_{16}\! \left(x \right) F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{168}\! \left(x \right)
F_{167}\! \left(x \right) = F_{26}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{16}\! \left(x \right) F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{167}\! \left(x \right)+F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{169}\! \left(x \right)
F_{172}\! \left(x \right) = F_{16}\! \left(x \right) F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{1}\! \left(x \right)+F_{174}\! \left(x \right)+F_{196}\! \left(x \right)+F_{230}\! \left(x \right)
F_{174}\! \left(x \right) = F_{16}\! \left(x \right) F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)+F_{180}\! \left(x \right)
F_{176}\! \left(x \right) = F_{13}\! \left(x \right)+F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{14}\! \left(x \right)+F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{153}\! \left(x \right)+F_{179}\! \left(x \right)+F_{42}\! \left(x \right)
F_{179}\! \left(x \right) = F_{16}\! \left(x \right) F_{177}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{56}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{52}\! \left(x \right)
F_{182}\! \left(x \right) = F_{156}\! \left(x \right)+F_{183}\! \left(x \right)+F_{185}\! \left(x \right)+F_{42}\! \left(x \right)
F_{183}\! \left(x \right) = F_{16}\! \left(x \right) F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{178}\! \left(x \right)+F_{182}\! \left(x \right)
F_{185}\! \left(x \right) = F_{16}\! \left(x \right) F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)+F_{52}\! \left(x \right)
F_{187}\! \left(x \right) = F_{185}\! \left(x \right)+F_{188}\! \left(x \right)+F_{193}\! \left(x \right)+F_{42}\! \left(x \right)
F_{188}\! \left(x \right) = F_{16}\! \left(x \right) F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{26}\! \left(x \right)
F_{190}\! \left(x \right) = 2 F_{42}\! \left(x \right)+F_{188}\! \left(x \right)+F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{16}\! \left(x \right) F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{190}\! \left(x \right)+F_{52}\! \left(x \right)
F_{193}\! \left(x \right) = F_{16}\! \left(x \right) F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{133}\! \left(x \right)+F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = 2 F_{42}\! \left(x \right)+F_{142}\! \left(x \right)+F_{193}\! \left(x \right)
F_{196}\! \left(x \right) = F_{16}\! \left(x \right) F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x , 1\right)
F_{198}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{199}\! \left(x , y\right)+F_{226}\! \left(x , y\right)+F_{228}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{200}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right)+F_{206}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{177}\! \left(x \right)+F_{203}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{204}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{205}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{203}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right)+F_{56}\! \left(x \right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = 2 F_{42}\! \left(x \right)+F_{210}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{211}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{208}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{181}\! \left(x \right)+F_{214}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = 3 F_{42}\! \left(x \right)+F_{216}\! \left(x , y\right)+F_{218}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{217}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{204}\! \left(x , y\right)+F_{215}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{220}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = 3 F_{42}\! \left(x \right)+F_{218}\! \left(x , y\right)+F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{222}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{223}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = 3 F_{42}\! \left(x \right)+F_{221}\! \left(x , y\right)+F_{224}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{225}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{223}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{227}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = -\frac{-y F_{198}\! \left(x , y\right)+F_{198}\! \left(x , 1\right)}{-1+y}
F_{228}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{229}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = -\frac{-y F_{72}\! \left(x , y\right)+F_{72}\! \left(x , 1\right)}{-1+y}
F_{230}\! \left(x \right) = F_{71}\! \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_16(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_172(x) + F_4(x))
Eq(F_4(x), F_16(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_123(x) + F_6(x) + F_85(x))
Eq(F_6(x), F_16(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_1(x) + F_69(x, k_0) + F_71(x, k_0) + F_79(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_16(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_34(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0) + F_24(x, k_0))
Eq(F_12(x, k_0), F_13(x) + F_17(x, k_0))
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x))
Eq(F_16(x), x)
Eq(F_17(x, k_0), F_18(x, k_0) + F_22(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_21(x, k_0))
Eq(F_20(x, k_0), F_1(x) + F_18(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_16(x)*F_17(x, k_0))
Eq(F_24(x, k_0), F_25(x) + F_28(x, k_0))
Eq(F_25(x), F_14(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_16(x)*F_25(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_21(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), F_14(x) + F_29(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_16(x)*F_28(x, k_0))
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_14(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_16(x)*F_39(x))
Eq(F_39(x), F_14(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_16(x)*F_44(x, k_0))
Eq(F_44(x, k_0), F_18(x, k_0) + F_41(x, k_0))
Eq(F_45(x, k_0), F_21(x, k_0)*F_46(x, k_0))
Eq(F_46(x, k_0), F_14(x) + F_41(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_16(x)*F_49(x, k_0))
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_16(x)*F_54(x))
Eq(F_54(x), F_14(x) + F_52(x))
Eq(F_55(x), F_16(x)*F_56(x))
Eq(F_56(x), F_14(x) + F_52(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_16(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_16(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_21(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_16(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_16(x)*F_70(x, k_0))
Eq(F_70(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_71(x, k_0), F_21(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_16(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_20(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_16(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_16(x)*F_80(x, k_0))
Eq(F_80(x, k_0), F_12(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_16(x)*F_82(x, k_0))
Eq(F_85(x), F_16(x)*F_86(x))
Eq(F_86(x), F_114(x) + F_87(x))
Eq(F_87(x), F_100(x) + F_88(x))
Eq(F_88(x), F_1(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_16(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), F_1(x) + F_16(x))
Eq(F_93(x), F_89(x) + F_94(x))
Eq(F_94(x), F_42(x) + F_95(x) + F_99(x))
Eq(F_95(x), F_16(x)*F_96(x))
Eq(F_96(x), F_97(x) + F_98(x))
Eq(F_97(x), F_16(x))
Eq(F_98(x), F_94(x))
Eq(F_99(x), F_16(x)*F_89(x))
Eq(F_100(x), F_101(x) + F_14(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_16(x))
Eq(F_103(x), F_104(x) + F_107(x))
Eq(F_104(x), F_105(x) + F_14(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_14(x)*F_16(x))
Eq(F_107(x), F_101(x) + F_108(x))
Eq(F_108(x), F_109(x) + F_113(x) + 2*F_42(x))
Eq(F_109(x), F_110(x)*F_16(x))
Eq(F_110(x), F_111(x) + F_112(x))
Eq(F_111(x), F_105(x))
Eq(F_112(x), F_108(x))
Eq(F_113(x), F_101(x)*F_16(x))
Eq(F_114(x), F_115(x) + F_119(x))
Eq(F_115(x), F_116(x) + F_14(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_16(x))
Eq(F_118(x), F_116(x) + F_89(x))
Eq(F_119(x), F_120(x) + F_52(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_122(x)*F_16(x))
Eq(F_122(x), F_101(x) + F_120(x))
Eq(F_123(x), F_124(x)*F_16(x))
Eq(F_124(x), F_125(x) + F_87(x))
Eq(F_125(x), F_126(x) + F_161(x))
Eq(F_126(x), F_127(x) + F_14(x))
Eq(F_127(x), F_128(x) + F_130(x) + F_42(x))
Eq(F_128(x), F_129(x)*F_16(x))
Eq(F_129(x), F_127(x) + F_89(x))
Eq(F_130(x), F_131(x)*F_16(x))
Eq(F_131(x), F_132(x) + F_136(x))
Eq(F_132(x), F_133(x) + F_14(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_16(x))
Eq(F_135(x), F_133(x) + F_16(x))
Eq(F_136(x), F_137(x) + F_149(x))
Eq(F_137(x), F_138(x) + F_42(x) + F_53(x))
Eq(F_138(x), F_139(x)*F_16(x))
Eq(F_139(x), F_132(x) + F_140(x))
Eq(F_140(x), F_137(x) + F_141(x))
Eq(F_141(x), F_142(x) + F_145(x) + 2*F_42(x))
Eq(F_142(x), F_143(x)*F_16(x))
Eq(F_143(x), F_105(x) + F_144(x))
Eq(F_144(x), F_142(x))
Eq(F_145(x), F_146(x)*F_16(x))
Eq(F_146(x), F_147(x) + F_148(x))
Eq(F_147(x), F_133(x))
Eq(F_148(x), F_141(x))
Eq(F_149(x), F_150(x) + F_158(x) + 2*F_42(x))
Eq(F_150(x), F_151(x)*F_16(x))
Eq(F_151(x), F_152(x) + F_155(x))
Eq(F_152(x), F_106(x) + F_153(x) + F_42(x))
Eq(F_153(x), F_154(x)*F_16(x))
Eq(F_154(x), F_152(x) + F_16(x))
Eq(F_155(x), F_150(x) + F_156(x) + 2*F_42(x))
Eq(F_156(x), F_157(x)*F_16(x))
Eq(F_157(x), F_133(x) + F_155(x))
Eq(F_158(x), F_159(x)*F_16(x))
Eq(F_159(x), F_147(x) + F_160(x))
Eq(F_160(x), F_149(x))
Eq(F_161(x), F_162(x) + F_52(x))
Eq(F_162(x), F_163(x) + F_165(x) + 2*F_42(x))
Eq(F_163(x), F_16(x)*F_164(x))
Eq(F_164(x), F_101(x) + F_162(x))
Eq(F_165(x), F_16(x)*F_166(x))
Eq(F_166(x), F_167(x) + F_168(x))
Eq(F_167(x), F_26(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_16(x)*F_170(x))
Eq(F_170(x), F_167(x) + F_171(x))
Eq(F_171(x), F_169(x))
Eq(F_172(x), F_16(x)*F_173(x))
Eq(F_173(x), F_1(x) + F_174(x) + F_196(x) + F_230(x))
Eq(F_174(x), F_16(x)*F_175(x))
Eq(F_175(x), F_176(x) + F_180(x))
Eq(F_176(x), F_13(x) + F_177(x))
Eq(F_177(x), F_14(x) + F_178(x))
Eq(F_178(x), F_153(x) + F_179(x) + F_42(x))
Eq(F_179(x), F_16(x)*F_177(x))
Eq(F_180(x), F_181(x) + F_56(x))
Eq(F_181(x), F_182(x) + F_52(x))
Eq(F_182(x), F_156(x) + F_183(x) + F_185(x) + F_42(x))
Eq(F_183(x), F_16(x)*F_184(x))
Eq(F_184(x), F_178(x) + F_182(x))
Eq(F_185(x), F_16(x)*F_186(x))
Eq(F_186(x), F_187(x) + F_52(x))
Eq(F_187(x), F_185(x) + F_188(x) + F_193(x) + F_42(x))
Eq(F_188(x), F_16(x)*F_189(x))
Eq(F_189(x), F_190(x) + F_26(x))
Eq(F_190(x), F_188(x) + F_191(x) + 2*F_42(x))
Eq(F_191(x), F_16(x)*F_192(x))
Eq(F_192(x), F_190(x) + F_52(x))
Eq(F_193(x), F_16(x)*F_194(x))
Eq(F_194(x), F_133(x) + F_195(x))
Eq(F_195(x), F_142(x) + F_193(x) + 2*F_42(x))
Eq(F_196(x), F_16(x)*F_197(x))
Eq(F_197(x), F_198(x, 1))
Eq(F_198(x, k_0), F_1(x) + F_199(x, k_0) + F_226(x, k_0) + F_228(x, k_0) + F_71(x, k_0))
Eq(F_199(x, k_0), F_16(x)*F_200(x, k_0))
Eq(F_200(x, k_0), F_201(x, k_0) + F_206(x, k_0))
Eq(F_201(x, k_0), F_12(x, k_0) + F_202(x, k_0))
Eq(F_202(x, k_0), F_177(x) + F_203(x, k_0))
Eq(F_203(x, k_0), F_204(x, k_0) + F_29(x, k_0))
Eq(F_204(x, k_0), F_205(x, k_0))
Eq(F_205(x, k_0), F_16(x)*F_203(x, k_0))
Eq(F_206(x, k_0), F_207(x, k_0) + F_213(x, k_0))
Eq(F_207(x, k_0), F_208(x, k_0) + F_56(x))
Eq(F_208(x, k_0), F_209(x, k_0) + F_41(x, k_0))
Eq(F_209(x, k_0), F_210(x, k_0) + F_212(x, k_0) + 2*F_42(x))
Eq(F_210(x, k_0), F_16(x)*F_211(x, k_0))
Eq(F_211(x, k_0), F_209(x, k_0) + F_22(x, k_0))
Eq(F_212(x, k_0), F_16(x)*F_208(x, k_0))
Eq(F_213(x, k_0), F_181(x) + F_214(x, k_0))
Eq(F_214(x, k_0), F_215(x, k_0) + F_61(x, k_0))
Eq(F_215(x, k_0), F_216(x, k_0) + F_218(x, k_0) + 3*F_42(x))
Eq(F_216(x, k_0), F_16(x)*F_217(x, k_0))
Eq(F_217(x, k_0), F_204(x, k_0) + F_215(x, k_0))
Eq(F_218(x, k_0), F_16(x)*F_219(x, k_0))
Eq(F_219(x, k_0), F_220(x, k_0) + F_61(x, k_0))
Eq(F_220(x, k_0), F_218(x, k_0) + F_221(x, k_0) + 3*F_42(x))
Eq(F_221(x, k_0), F_16(x)*F_222(x, k_0))
Eq(F_222(x, k_0), F_223(x, k_0) + F_32(x, k_0))
Eq(F_223(x, k_0), F_221(x, k_0) + F_224(x, k_0) + 3*F_42(x))
Eq(F_224(x, k_0), F_16(x)*F_225(x, k_0))
Eq(F_225(x, k_0), F_223(x, k_0) + F_61(x, k_0))
Eq(F_226(x, k_0), F_16(x)*F_227(x, k_0))
Eq(F_227(x, k_0), (k_0*F_198(x, k_0) - F_198(x, 1))/(k_0 - 1))
Eq(F_228(x, k_0), F_16(x)*F_229(x, k_0))
Eq(F_229(x, k_0), (-k_0*F_72(x, k_0) + F_72(x, 1))/(1 - k_0))
Eq(F_230(x), F_71(x, 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": 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:
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