0213_1230_3012
Counting sequence:
1, 1, 2, 6, 21, 72, 230, 701, 2113, 6475, 20468, 66969, 226027, 782276, 2760094, 9880455, 35758457, 130507165, 479487736, 1771213935, 6572533275, 24484124014, 91520352034, 343139355270, 1290071981495, 4862298799421, 18368091363064, 69535094533135, 263751173112167, 1002248927700780, 3815000460929710, 14544665030484971, 55534125006859177, 212336254966608945, 812944299848134112, 3116286027483669371, 11959799485372569563, 45950806592365035538, 176733867459931761290, 680425381350703275294, 2622127062067702240479, 10113918632319829303833, 39044429995467328734128, 150853479376609166791739, 583300119944840415321575, 2257117854798527702581328, 8740328713010917019460246, 33868773760216902887944580, 131327898248361814967711631, 509552245192283512008901483, 1978261657782056351483715796, 7684785670567233680855248797, 29869166945880712341202429055, 116157871456003110632298433474, 451959718028403831410350330666, 1759414616609737605316467593280, 6852456927846746994994649118867, 26700952856778670956729236042737, 104088460289130086253654420430624, 405944995127592838401331793398875, 1583850964596152324488901777158559, 6182127958584921367012843444452668, 24139737743045760564605992948073294, 94295850558772251877410472170448883, 368479169875817212881331254008951049, 1440418573150920794123878390536086297, 5632681584560315022390180845843880240, 22033725021956522111938059188875102099, 86218923998960295170918606403003540955, 337485502510215994741397630113005222810, 1321422108420282309449465660864816442074, 5175569924646105638518578782061637954270, 20276890389709400023489458985822594283407, 79463489365077378167051524950354805767153, 311496878311103321798667599120559482292576, 1221395654430378813169912803142941391106227, 4790408930363303914048469302527780125086759, 18793142726809884580727085331079290825241112, 73745243611532458470872715686082649129258598, 289450081175264899476951205147265064315599552, 1136359577947336271977572058150023365333572807, 4462290049988320482556328585616459629980897291, 17526585015616776834923732945775537787681095956, 68854441132780194708270072593666869962224978877, 270557451039395118029416175813721929092517872303, 1063353702922273835974603425905697018133559364506, 4180080073556524734517868049521576245383219294874, 16435314834665426797075566774716679053543670901248, 64633260585762914370509635856558677955568019798979, 254224158304000796523979747004676461417389024697609, 1000134600800354781929452481958231135714281801238608, 3935312233584004685417961273546767337857947955563699, 15487357822491889407128544841225257458942313428343071, 60960876535340415751463004287483634487347593053347012, 239993345518077005168916667940305008480078754918531230, 944973797977428207852607672895636796350911011423947856, 3721443204405954385563874185874722315869036000468039423, 14657929356129575437016885214876146588296351150558369271, 57743358069601357782187715502937409015716199211094262252, 227508830794229349661819570502390609376489968148321074921, 896519947090131496687170130921329443375848793380582740591
Generating function in Maple syntax:
1/2*(-4*(x-1)^6*(x-1/2)^2*(1-4*x)^(1/2)-8*x^9+22*x^8-38*x^7+91*x^6-152*x^5+157*x^4-104*x^3+43*x^2-10*x+1)/x/(2*x-1)^2/(x-1)^6
Generating function in latex syntax:
\frac{-4 \left(x -1\right)^{6} \left(x -\frac{1}{2}\right)^{2} \sqrt{1-4 x}-8 x^{9}+22 x^{8}-38 x^{7}+91 x^{6}-152 x^{5}+157 x^{4}-104 x^{3}+43 x^{2}-10 x +1}{2 x \left(2 x -1\right)^{2} \left(x -1\right)^{6}}
Generating function in sympy syntax:
(-4*x**9 + 11*x**8 - 19*x**7 + 91*x**6/2 - 76*x**5 + 157*x**4/2 - 52*x**3 + 43*x**2/2 - 5*x - 2*sqrt(1 - 4*x)*(x - 1)**6*(x - 1/2)**2 + 1/2)/(x*(x - 1)**6*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^4*(x-1)^12*F(x)^2+(8*x^9-22*x^8+38*x^7-91*x^6+152*x^5-157*x^4+104*x^3-43*x^2+10*x-1)*(2*x-1)^2*(x-1)^6*F(x)+16*x^17-72*x^16+45*x^15+738*x^14-4324*x^13+14094*x^12-31391*x^11+51202*x^10-63478*x^9+61033*x^8-45896*x^7+26968*x^6-12260*x^5+4226*x^4-1067*x^3+186*x^2-20*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{4} \left(x -1\right)^{12} F \! \left(x \right)^{2}+\left(8 x^{9}-22 x^{8}+38 x^{7}-91 x^{6}+152 x^{5}-157 x^{4}+104 x^{3}-43 x^{2}+10 x -1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{6} F \! \left(x \right)+16 x^{17}-72 x^{16}+45 x^{15}+738 x^{14}-4324 x^{13}+14094 x^{12}-31391 x^{11}+51202 x^{10}-63478 x^{9}+61033 x^{8}-45896 x^{7}+26968 x^{6}-12260 x^{5}+4226 x^{4}-1067 x^{3}+186 x^{2}-20 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 72
a(6) = 230
a(7) = 701
a(8) = 2113
a(9) = 6475
a(10) = 20468
a(11) = 66969
a(n+4) = -16*(2*n+1)/(n+5)*a(n)+8*(7*n+11)/(n+5)*a(n+1)-12*(3*n+8)/(n+5)*a(n+2)+2*(5*n+19)/(n+5)*a(n+3)+1/120*(3*n^6-59*n^5+55*n^4+2895*n^3-9298*n^2+1964*n+1560)/(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) = 21
a \! \left(5\right) = 72
a \! \left(6\right) = 230
a \! \left(7\right) = 701
a \! \left(8\right) = 2113
a \! \left(9\right) = 6475
a \! \left(10\right) = 20468
a \! \left(11\right) = 66969
a \! \left(n +4\right) = -\frac{16 \left(2 n +1\right) a \! \left(n \right)}{n +5}+\frac{8 \left(7 n +11\right) a \! \left(n +1\right)}{n +5}-\frac{12 \left(3 n +8\right) a \! \left(n +2\right)}{n +5}+\frac{2 \left(5 n +19\right) a \! \left(n +3\right)}{n +5}+\frac{3 n^{6}-59 n^{5}+55 n^{4}+2895 n^{3}-9298 n^{2}+1964 n +1560}{120 n +600}, \quad n \geq 12
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/330/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[12,x]*F[3,x]
F[3,x] = F[1,x]+F[115,x]+F[4,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[1,x]+F[114,x]+F[48,x]+F[6,x]
F[6,x] = F[12,x]*F[7,x]
F[7,x] = F[22,x]+F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[10,x]+F[14,x]
F[14,x] = F[15,x]+F[16,x]+F[21,x]
F[15,x] = 0
F[16,x] = F[12,x]*F[17,x]
F[17,x] = F[10,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[10,x]+F[18,x]
F[21,x] = F[12,x]*F[13,x]
F[22,x] = F[23,x]+F[28,x]
F[23,x] = F[10,x]+F[24,x]
F[24,x] = F[15,x]+F[25,x]+F[27,x]
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[10,x]+F[24,x]
F[27,x] = F[12,x]*F[23,x]
F[28,x] = F[24,x]+F[29,x]
F[29,x] = F[15,x]+F[30,x]+F[32,x]+F[40,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[14,x]+F[29,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[35,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[10,x]+F[34,x]
F[37,x] = F[38,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[18,x]+F[37,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[24,x]+F[42,x]
F[42,x] = F[15,x]+F[32,x]+F[40,x]+F[43,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[18,x]+F[45,x]
F[45,x] = 2*F[15,x]+F[43,x]+F[46,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[24,x]+F[45,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[50,x,1]
F[50,x,k[0]] = F[1,x]+F[102,x,k[0]]+F[104,x,k[0]]+F[112,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = F[12,x]*F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]+F[69,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[62,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[9,x]
F[55,x,k[0]] = F[56,x,k[0]]+F[60,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]*F[59,x,k[0]]
F[58,x,k[0]] = F[1,x]+F[56,x,k[0]]
F[59,x,k[0]] = k[0]*x
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[12,x]*F[55,x,k[0]]
F[62,x,k[0]] = F[13,x]+F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[67,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[59,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[10,x]+F[64,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[12,x]*F[63,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]+F[81,x,k[0]]
F[70,x,k[0]] = F[23,x]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]+F[77,x,k[0]]
F[72,x,k[0]] = F[15,x]+F[73,x,k[0]]+F[75,x,k[0]]
F[73,x,k[0]] = F[12,x]*F[74,x,k[0]]
F[74,x,k[0]] = F[56,x,k[0]]+F[72,x,k[0]]
F[75,x,k[0]] = F[59,x,k[0]]*F[76,x,k[0]]
F[76,x,k[0]] = F[10,x]+F[72,x,k[0]]
F[77,x,k[0]] = 2*F[15,x]+F[78,x,k[0]]+F[80,x,k[0]]
F[78,x,k[0]] = F[12,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[60,x,k[0]]+F[77,x,k[0]]
F[80,x,k[0]] = F[12,x]*F[71,x,k[0]]
F[81,x,k[0]] = F[28,x]+F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]+F[88,x,k[0]]
F[83,x,k[0]] = 2*F[15,x]+F[84,x,k[0]]+F[86,x,k[0]]
F[84,x,k[0]] = F[12,x]*F[85,x,k[0]]
F[85,x,k[0]] = F[64,x,k[0]]+F[83,x,k[0]]
F[86,x,k[0]] = F[59,x,k[0]]*F[87,x,k[0]]
F[87,x,k[0]] = F[24,x]+F[83,x,k[0]]
F[88,x,k[0]] = 3*F[15,x]+F[89,x,k[0]]+F[91,x,k[0]]
F[89,x,k[0]] = F[12,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[67,x,k[0]]+F[88,x,k[0]]
F[91,x,k[0]] = F[12,x]*F[92,x,k[0]]
F[92,x,k[0]] = F[83,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = 3*F[15,x]+F[91,x,k[0]]+F[94,x,k[0]]
F[94,x,k[0]] = F[12,x]*F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]+F[99,x,k[0]]
F[96,x,k[0]] = F[97,x,k[0]]
F[97,x,k[0]] = F[12,x]*F[98,x,k[0]]
F[98,x,k[0]] = F[64,x,k[0]]+F[96,x,k[0]]
F[99,x,k[0]] = 3*F[15,x]+F[100,x,k[0]]+F[94,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[12,x]
F[101,x,k[0]] = F[83,x,k[0]]+F[99,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[12,x]
F[103,x,k[0]] = 1/(-1+k[0])*(F[50,x,k[0]]*k[0]-F[50,x,1])
F[104,x,k[0]] = F[105,x,k[0]]*F[59,x,k[0]]
F[105,x,k[0]] = F[1,x]+F[104,x,k[0]]+F[106,x,k[0]]+F[110,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[12,x]
F[107,x,k[0]] = F[108,x,k[0]]+F[109,x,k[0]]
F[108,x,k[0]] = F[58,x,k[0]]+F[66,x,k[0]]
F[109,x,k[0]] = F[76,x,k[0]]+F[87,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]*F[12,x]
F[111,x,k[0]] = 1/(-1+k[0])*(F[105,x,k[0]]*k[0]-F[105,x,1])
F[112,x,k[0]] = F[113,x,k[0]]*F[12,x]
F[113,x,k[0]] = 1/(-1+k[0])*(F[105,x,k[0]]*k[0]-F[105,x,1])
F[114,x] = F[104,x,1]
F[115,x] = F[116,x]*F[12,x]
F[116,x] = F[117,x]+F[142,x]
F[117,x] = F[118,x]+F[125,x]
F[118,x] = F[1,x]+F[119,x]
F[119,x] = F[120,x]
F[120,x] = F[12,x]*F[121,x]
F[121,x] = F[122,x]+F[9,x]
F[122,x] = F[119,x]+F[123,x]
F[123,x] = F[124,x]
F[124,x] = F[12,x]*F[122,x]
F[125,x] = F[126,x]+F[129,x]
F[126,x] = F[127,x]
F[127,x] = F[12,x]*F[128,x]
F[128,x] = F[1,x]+F[126,x]
F[129,x] = F[130,x]+F[132,x]+F[15,x]
F[130,x] = F[12,x]*F[131,x]
F[131,x] = F[119,x]+F[129,x]
F[132,x] = F[12,x]*F[133,x]
F[133,x] = F[134,x]+F[137,x]
F[134,x] = F[12,x]+F[135,x]
F[135,x] = F[136,x]
F[136,x] = F[12,x]*F[134,x]
F[137,x] = F[138,x]+F[140,x]
F[138,x] = F[132,x]+F[139,x]+F[15,x]
F[139,x] = F[10,x]*F[12,x]
F[140,x] = F[141,x]
F[141,x] = F[12,x]*F[137,x]
F[142,x] = F[143,x]+F[197,x]
F[143,x] = F[144,x]+F[155,x]
F[144,x] = F[145,x]
F[145,x] = F[12,x]*F[146,x]
F[146,x] = F[147,x]+F[148,x]
F[147,x] = F[1,x]+F[12,x]
F[148,x] = F[144,x]+F[149,x]
F[149,x] = F[15,x]+F[150,x]+F[154,x]
F[150,x] = F[12,x]*F[151,x]
F[151,x] = F[152,x]+F[153,x]
F[152,x] = F[12,x]
F[153,x] = F[149,x]
F[154,x] = F[12,x]*F[144,x]
F[155,x] = F[15,x]+F[156,x]+F[191,x]
F[156,x] = F[12,x]*F[157,x]
F[157,x] = F[158,x]+F[166,x]
F[158,x] = F[119,x]+F[159,x]
F[159,x] = F[15,x]+F[160,x]+F[161,x]
F[160,x] = F[119,x]*F[12,x]
F[161,x] = F[12,x]*F[162,x]
F[162,x] = F[163,x]+F[164,x]
F[163,x] = F[12,x]
F[164,x] = F[165,x]
F[165,x] = F[139,x]+F[15,x]+F[161,x]
F[166,x] = F[155,x]+F[167,x]
F[167,x] = F[15,x]+F[168,x]+F[172,x]+F[184,x]
F[168,x] = F[12,x]*F[169,x]
F[169,x] = F[170,x]+F[171,x]
F[170,x] = F[159,x]
F[171,x] = F[167,x]
F[172,x] = F[12,x]*F[173,x]
F[173,x] = F[174,x]
F[174,x] = F[12,x]*F[175,x]
F[175,x] = F[176,x]+F[178,x]
F[176,x] = F[119,x]+F[177,x]
F[177,x] = F[160,x]
F[178,x] = F[173,x]+F[179,x]
F[179,x] = 2*F[15,x]+F[172,x]+F[180,x]
F[180,x] = F[12,x]*F[181,x]
F[181,x] = F[182,x]+F[183,x]
F[182,x] = F[177,x]
F[183,x] = F[179,x]
F[184,x] = F[12,x]*F[185,x]
F[185,x] = F[186,x]+F[188,x]
F[186,x] = F[187,x]
F[187,x] = F[10,x]*F[12,x]
F[188,x] = F[189,x]
F[189,x] = 2*F[15,x]+F[184,x]+F[190,x]
F[190,x] = F[12,x]*F[34,x]
F[191,x] = F[12,x]*F[192,x]
F[192,x] = F[193,x]+F[194,x]
F[193,x] = F[10,x]+F[34,x]
F[194,x] = F[195,x]+F[196,x]
F[195,x] = F[15,x]+F[191,x]+F[25,x]
F[196,x] = F[38,x]
F[197,x] = F[198,x]+F[221,x]
F[198,x] = F[15,x]+F[199,x]+F[219,x]
F[199,x] = F[12,x]*F[200,x]
F[200,x] = F[201,x]+F[204,x]
F[201,x] = F[126,x]+F[202,x]
F[202,x] = F[203,x]
F[203,x] = F[12,x]*F[126,x]
F[204,x] = F[198,x]+F[205,x]
F[205,x] = 2*F[15,x]+F[206,x]+F[210,x]
F[206,x] = F[12,x]*F[207,x]
F[207,x] = F[208,x]+F[209,x]
F[208,x] = F[202,x]
F[209,x] = F[205,x]
F[210,x] = F[12,x]*F[211,x]
F[211,x] = F[212,x]
F[212,x] = F[12,x]*F[213,x]
F[213,x] = F[201,x]+F[214,x]
F[214,x] = F[211,x]+F[215,x]
F[215,x] = 2*F[15,x]+F[210,x]+F[216,x]
F[216,x] = F[12,x]*F[217,x]
F[217,x] = F[208,x]+F[218,x]
F[218,x] = F[215,x]
F[219,x] = F[12,x]*F[220,x]
F[220,x] = F[144,x]+F[211,x]
F[221,x] = F[15,x]+F[222,x]+F[246,x]+F[248,x]
F[222,x] = F[12,x]*F[223,x]
F[223,x] = F[224,x]+F[227,x]
F[224,x] = F[129,x]+F[225,x]
F[225,x] = F[226,x]
F[226,x] = F[12,x]*F[129,x]
F[227,x] = F[221,x]+F[228,x]
F[228,x] = 2*F[15,x]+F[229,x]+F[233,x]+F[245,x]
F[229,x] = F[12,x]*F[230,x]
F[230,x] = F[231,x]+F[232,x]
F[231,x] = F[225,x]
F[232,x] = F[228,x]
F[233,x] = F[12,x]*F[234,x]
F[234,x] = F[235,x]
F[235,x] = F[12,x]*F[236,x]
F[236,x] = F[237,x]+F[239,x]
F[237,x] = F[129,x]+F[238,x]
F[238,x] = F[226,x]
F[239,x] = F[234,x]+F[240,x]
F[240,x] = 3*F[15,x]+F[233,x]+F[241,x]
F[241,x] = F[12,x]*F[242,x]
F[242,x] = F[243,x]+F[244,x]
F[243,x] = F[238,x]
F[244,x] = F[240,x]
F[245,x] = 0
F[246,x] = F[12,x]*F[247,x]
F[247,x] = F[173,x]+F[234,x]
F[248,x] = F[12,x]*F[249,x]
F[249,x] = F[250,x]+F[251,x]
F[250,x] = F[187,x]
F[251,x] = F[252,x]
F[252,x] = 2*F[15,x]+F[190,x]+F[248,x]
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_{12}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{115}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{114}\! \left(x \right)+F_{48}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{12}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{22}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{21}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{10}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{10}\! \left(x \right)+F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)
F_{23}\! \left(x \right) = F_{10}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{10}\! \left(x \right)+F_{24}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{15}\! \left(x \right)+F_{30}\! \left(x \right)+F_{32}\! \left(x \right)+F_{40}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{10}\! \left(x \right)+F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{18}\! \left(x \right)+F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{24}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right)+F_{32}\! \left(x \right)+F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{18}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{24}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x , 1\right)
F_{50}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{102}\! \left(x , y\right)+F_{104}\! \left(x , y\right)+F_{112}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{56}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = y x
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{13}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{59}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{64}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{73}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{59}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{59}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = 3 F_{15}\! \left(x \right)+F_{89}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{67}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = 3 F_{15}\! \left(x \right)+F_{91}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = 3 F_{15}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{101}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{103}\! \left(x , y\right) = -\frac{-y F_{50}\! \left(x , y\right)+F_{50}\! \left(x , 1\right)}{-1+y}
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{104}\! \left(x , y\right)+F_{106}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{109}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{111}\! \left(x , y\right) = -\frac{-y F_{105}\! \left(x , y\right)+F_{105}\! \left(x , 1\right)}{-1+y}
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{113}\! \left(x , y\right) = -\frac{-y F_{105}\! \left(x , y\right)+F_{105}\! \left(x , 1\right)}{-1+y}
F_{114}\! \left(x \right) = F_{104}\! \left(x , 1\right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{12}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{142}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{125}\! \left(x \right)
F_{118}\! \left(x \right) = F_{1}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{12}\! \left(x \right) F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{9}\! \left(x \right)
F_{122}\! \left(x \right) = F_{119}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{12}\! \left(x \right) F_{122}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{129}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{12}\! \left(x \right) F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{1}\! \left(x \right)+F_{126}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)+F_{15}\! \left(x \right)
F_{130}\! \left(x \right) = F_{12}\! \left(x \right) F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{119}\! \left(x \right)+F_{129}\! \left(x \right)
F_{132}\! \left(x \right) = F_{12}\! \left(x \right) F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{137}\! \left(x \right)
F_{134}\! \left(x \right) = F_{12}\! \left(x \right)+F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{12}\! \left(x \right) F_{134}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{140}\! \left(x \right)
F_{138}\! \left(x \right) = F_{132}\! \left(x \right)+F_{139}\! \left(x \right)+F_{15}\! \left(x \right)
F_{139}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{12}\! \left(x \right) F_{137}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{197}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{155}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{12}\! \left(x \right) F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{148}\! \left(x \right)
F_{147}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{148}\! \left(x \right) = F_{144}\! \left(x \right)+F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{15}\! \left(x \right)+F_{150}\! \left(x \right)+F_{154}\! \left(x \right)
F_{150}\! \left(x \right) = F_{12}\! \left(x \right) F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{153}\! \left(x \right)
F_{152}\! \left(x \right) = F_{12}\! \left(x \right)
F_{153}\! \left(x \right) = F_{149}\! \left(x \right)
F_{154}\! \left(x \right) = F_{12}\! \left(x \right) F_{144}\! \left(x \right)
F_{155}\! \left(x \right) = F_{15}\! \left(x \right)+F_{156}\! \left(x \right)+F_{191}\! \left(x \right)
F_{156}\! \left(x \right) = F_{12}\! \left(x \right) F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{166}\! \left(x \right)
F_{158}\! \left(x \right) = F_{119}\! \left(x \right)+F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{15}\! \left(x \right)+F_{160}\! \left(x \right)+F_{161}\! \left(x \right)
F_{160}\! \left(x \right) = F_{119}\! \left(x \right) F_{12}\! \left(x \right)
F_{161}\! \left(x \right) = F_{12}\! \left(x \right) F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{164}\! \left(x \right)
F_{163}\! \left(x \right) = F_{12}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{139}\! \left(x \right)+F_{15}\! \left(x \right)+F_{161}\! \left(x \right)
F_{166}\! \left(x \right) = F_{155}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{15}\! \left(x \right)+F_{168}\! \left(x \right)+F_{172}\! \left(x \right)+F_{184}\! \left(x \right)
F_{168}\! \left(x \right) = F_{12}\! \left(x \right) F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{171}\! \left(x \right)
F_{170}\! \left(x \right) = F_{159}\! \left(x \right)
F_{171}\! \left(x \right) = F_{167}\! \left(x \right)
F_{172}\! \left(x \right) = F_{12}\! \left(x \right) F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{12}\! \left(x \right) F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)+F_{178}\! \left(x \right)
F_{176}\! \left(x \right) = F_{119}\! \left(x \right)+F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{160}\! \left(x \right)
F_{178}\! \left(x \right) = F_{173}\! \left(x \right)+F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{172}\! \left(x \right)+F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{12}\! \left(x \right) F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{183}\! \left(x \right)
F_{182}\! \left(x \right) = F_{177}\! \left(x \right)
F_{183}\! \left(x \right) = F_{179}\! \left(x \right)
F_{184}\! \left(x \right) = F_{12}\! \left(x \right) F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{188}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{184}\! \left(x \right)+F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{191}\! \left(x \right) = F_{12}\! \left(x \right) F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{194}\! \left(x \right)
F_{193}\! \left(x \right) = F_{10}\! \left(x \right)+F_{34}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)+F_{196}\! \left(x \right)
F_{195}\! \left(x \right) = F_{15}\! \left(x \right)+F_{191}\! \left(x \right)+F_{25}\! \left(x \right)
F_{196}\! \left(x \right) = F_{38}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)+F_{221}\! \left(x \right)
F_{198}\! \left(x \right) = F_{15}\! \left(x \right)+F_{199}\! \left(x \right)+F_{219}\! \left(x \right)
F_{199}\! \left(x \right) = F_{12}\! \left(x \right) F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{204}\! \left(x \right)
F_{201}\! \left(x \right) = F_{126}\! \left(x \right)+F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = F_{12}\! \left(x \right) F_{126}\! \left(x \right)
F_{204}\! \left(x \right) = F_{198}\! \left(x \right)+F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{206}\! \left(x \right)+F_{210}\! \left(x \right)
F_{206}\! \left(x \right) = F_{12}\! \left(x \right) F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{209}\! \left(x \right)
F_{208}\! \left(x \right) = F_{202}\! \left(x \right)
F_{209}\! \left(x \right) = F_{205}\! \left(x \right)
F_{210}\! \left(x \right) = F_{12}\! \left(x \right) F_{211}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{12}\! \left(x \right) F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{201}\! \left(x \right)+F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = F_{211}\! \left(x \right)+F_{215}\! \left(x \right)
F_{215}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{210}\! \left(x \right)+F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = F_{12}\! \left(x \right) F_{217}\! \left(x \right)
F_{217}\! \left(x \right) = F_{208}\! \left(x \right)+F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{215}\! \left(x \right)
F_{219}\! \left(x \right) = F_{12}\! \left(x \right) F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{144}\! \left(x \right)+F_{211}\! \left(x \right)
F_{221}\! \left(x \right) = F_{15}\! \left(x \right)+F_{222}\! \left(x \right)+F_{246}\! \left(x \right)+F_{248}\! \left(x \right)
F_{222}\! \left(x \right) = F_{12}\! \left(x \right) F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right)+F_{227}\! \left(x \right)
F_{224}\! \left(x \right) = F_{129}\! \left(x \right)+F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right)
F_{226}\! \left(x \right) = F_{12}\! \left(x \right) F_{129}\! \left(x \right)
F_{227}\! \left(x \right) = F_{221}\! \left(x \right)+F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{229}\! \left(x \right)+F_{233}\! \left(x \right)+F_{245}\! \left(x \right)
F_{229}\! \left(x \right) = F_{12}\! \left(x \right) F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)+F_{232}\! \left(x \right)
F_{231}\! \left(x \right) = F_{225}\! \left(x \right)
F_{232}\! \left(x \right) = F_{228}\! \left(x \right)
F_{233}\! \left(x \right) = F_{12}\! \left(x \right) F_{234}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{12}\! \left(x \right) F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right)+F_{239}\! \left(x \right)
F_{237}\! \left(x \right) = F_{129}\! \left(x \right)+F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = F_{226}\! \left(x \right)
F_{239}\! \left(x \right) = F_{234}\! \left(x \right)+F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{233}\! \left(x \right)+F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{12}\! \left(x \right) F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)+F_{244}\! \left(x \right)
F_{243}\! \left(x \right) = F_{238}\! \left(x \right)
F_{244}\! \left(x \right) = F_{240}\! \left(x \right)
F_{245}\! \left(x \right) = 0
F_{246}\! \left(x \right) = F_{12}\! \left(x \right) F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{173}\! \left(x \right)+F_{234}\! \left(x \right)
F_{248}\! \left(x \right) = F_{12}\! \left(x \right) F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right)+F_{251}\! \left(x \right)
F_{250}\! \left(x \right) = F_{187}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)
F_{252}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{190}\! \left(x \right)+F_{248}\! \left(x \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_12(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_115(x) + F_4(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_114(x) + F_48(x) + F_6(x))
Eq(F_6(x), F_12(x)*F_7(x))
Eq(F_7(x), F_22(x) + F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_10(x) + F_14(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_21(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_12(x)*F_17(x))
Eq(F_17(x), F_10(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_10(x) + F_18(x))
Eq(F_21(x), F_12(x)*F_13(x))
Eq(F_22(x), F_23(x) + F_28(x))
Eq(F_23(x), F_10(x) + F_24(x))
Eq(F_24(x), F_15(x) + F_25(x) + F_27(x))
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_10(x) + F_24(x))
Eq(F_27(x), F_12(x)*F_23(x))
Eq(F_28(x), F_24(x) + F_29(x))
Eq(F_29(x), F_15(x) + F_30(x) + F_32(x) + F_40(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_14(x) + F_29(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_10(x) + F_34(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_18(x) + F_37(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_24(x) + F_42(x))
Eq(F_42(x), F_15(x) + F_32(x) + F_40(x) + F_43(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_18(x) + F_45(x))
Eq(F_45(x), 2*F_15(x) + F_43(x) + F_46(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_24(x) + F_45(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_50(x, 1))
Eq(F_50(x, k_0), F_1(x) + F_102(x, k_0) + F_104(x, k_0) + F_112(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), F_12(x)*F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0) + F_69(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_62(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_9(x))
Eq(F_55(x, k_0), F_56(x, k_0) + F_60(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0)*F_59(x, k_0))
Eq(F_58(x, k_0), F_1(x) + F_56(x, k_0))
Eq(F_59(x, k_0), k_0*x)
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_12(x)*F_55(x, k_0))
Eq(F_62(x, k_0), F_13(x) + F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_67(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_59(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_10(x) + F_64(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_12(x)*F_63(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0) + F_81(x, k_0))
Eq(F_70(x, k_0), F_23(x) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0) + F_77(x, k_0))
Eq(F_72(x, k_0), F_15(x) + F_73(x, k_0) + F_75(x, k_0))
Eq(F_73(x, k_0), F_12(x)*F_74(x, k_0))
Eq(F_74(x, k_0), F_56(x, k_0) + F_72(x, k_0))
Eq(F_75(x, k_0), F_59(x, k_0)*F_76(x, k_0))
Eq(F_76(x, k_0), F_10(x) + F_72(x, k_0))
Eq(F_77(x, k_0), 2*F_15(x) + F_78(x, k_0) + F_80(x, k_0))
Eq(F_78(x, k_0), F_12(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_60(x, k_0) + F_77(x, k_0))
Eq(F_80(x, k_0), F_12(x)*F_71(x, k_0))
Eq(F_81(x, k_0), F_28(x) + F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0) + F_88(x, k_0))
Eq(F_83(x, k_0), 2*F_15(x) + F_84(x, k_0) + F_86(x, k_0))
Eq(F_84(x, k_0), F_12(x)*F_85(x, k_0))
Eq(F_85(x, k_0), F_64(x, k_0) + F_83(x, k_0))
Eq(F_86(x, k_0), F_59(x, k_0)*F_87(x, k_0))
Eq(F_87(x, k_0), F_24(x) + F_83(x, k_0))
Eq(F_88(x, k_0), 3*F_15(x) + F_89(x, k_0) + F_91(x, k_0))
Eq(F_89(x, k_0), F_12(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_67(x, k_0) + F_88(x, k_0))
Eq(F_91(x, k_0), F_12(x)*F_92(x, k_0))
Eq(F_92(x, k_0), F_83(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), 3*F_15(x) + F_91(x, k_0) + F_94(x, k_0))
Eq(F_94(x, k_0), F_12(x)*F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0) + F_99(x, k_0))
Eq(F_96(x, k_0), F_97(x, k_0))
Eq(F_97(x, k_0), F_12(x)*F_98(x, k_0))
Eq(F_98(x, k_0), F_64(x, k_0) + F_96(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + 3*F_15(x) + F_94(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0)*F_12(x))
Eq(F_101(x, k_0), F_83(x, k_0) + F_99(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_12(x))
Eq(F_103(x, k_0), (k_0*F_50(x, k_0) - F_50(x, 1))/(k_0 - 1))
Eq(F_104(x, k_0), F_105(x, k_0)*F_59(x, k_0))
Eq(F_105(x, k_0), F_1(x) + F_104(x, k_0) + F_106(x, k_0) + F_110(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_12(x))
Eq(F_107(x, k_0), F_108(x, k_0) + F_109(x, k_0))
Eq(F_108(x, k_0), F_58(x, k_0) + F_66(x, k_0))
Eq(F_109(x, k_0), F_76(x, k_0) + F_87(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0)*F_12(x))
Eq(F_111(x, k_0), (k_0*F_105(x, k_0) - F_105(x, 1))/(k_0 - 1))
Eq(F_112(x, k_0), F_113(x, k_0)*F_12(x))
Eq(F_113(x, k_0), (-k_0*F_105(x, k_0) + F_105(x, 1))/(1 - k_0))
Eq(F_114(x), F_104(x, 1))
Eq(F_115(x), F_116(x)*F_12(x))
Eq(F_116(x), F_117(x) + F_142(x))
Eq(F_117(x), F_118(x) + F_125(x))
Eq(F_118(x), F_1(x) + F_119(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_12(x)*F_121(x))
Eq(F_121(x), F_122(x) + F_9(x))
Eq(F_122(x), F_119(x) + F_123(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_12(x)*F_122(x))
Eq(F_125(x), F_126(x) + F_129(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_12(x)*F_128(x))
Eq(F_128(x), F_1(x) + F_126(x))
Eq(F_129(x), F_130(x) + F_132(x) + F_15(x))
Eq(F_130(x), F_12(x)*F_131(x))
Eq(F_131(x), F_119(x) + F_129(x))
Eq(F_132(x), F_12(x)*F_133(x))
Eq(F_133(x), F_134(x) + F_137(x))
Eq(F_134(x), F_12(x) + F_135(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_12(x)*F_134(x))
Eq(F_137(x), F_138(x) + F_140(x))
Eq(F_138(x), F_132(x) + F_139(x) + F_15(x))
Eq(F_139(x), F_10(x)*F_12(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_12(x)*F_137(x))
Eq(F_142(x), F_143(x) + F_197(x))
Eq(F_143(x), F_144(x) + F_155(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_12(x)*F_146(x))
Eq(F_146(x), F_147(x) + F_148(x))
Eq(F_147(x), F_1(x) + F_12(x))
Eq(F_148(x), F_144(x) + F_149(x))
Eq(F_149(x), F_15(x) + F_150(x) + F_154(x))
Eq(F_150(x), F_12(x)*F_151(x))
Eq(F_151(x), F_152(x) + F_153(x))
Eq(F_152(x), F_12(x))
Eq(F_153(x), F_149(x))
Eq(F_154(x), F_12(x)*F_144(x))
Eq(F_155(x), F_15(x) + F_156(x) + F_191(x))
Eq(F_156(x), F_12(x)*F_157(x))
Eq(F_157(x), F_158(x) + F_166(x))
Eq(F_158(x), F_119(x) + F_159(x))
Eq(F_159(x), F_15(x) + F_160(x) + F_161(x))
Eq(F_160(x), F_119(x)*F_12(x))
Eq(F_161(x), F_12(x)*F_162(x))
Eq(F_162(x), F_163(x) + F_164(x))
Eq(F_163(x), F_12(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_139(x) + F_15(x) + F_161(x))
Eq(F_166(x), F_155(x) + F_167(x))
Eq(F_167(x), F_15(x) + F_168(x) + F_172(x) + F_184(x))
Eq(F_168(x), F_12(x)*F_169(x))
Eq(F_169(x), F_170(x) + F_171(x))
Eq(F_170(x), F_159(x))
Eq(F_171(x), F_167(x))
Eq(F_172(x), F_12(x)*F_173(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_12(x)*F_175(x))
Eq(F_175(x), F_176(x) + F_178(x))
Eq(F_176(x), F_119(x) + F_177(x))
Eq(F_177(x), F_160(x))
Eq(F_178(x), F_173(x) + F_179(x))
Eq(F_179(x), 2*F_15(x) + F_172(x) + F_180(x))
Eq(F_180(x), F_12(x)*F_181(x))
Eq(F_181(x), F_182(x) + F_183(x))
Eq(F_182(x), F_177(x))
Eq(F_183(x), F_179(x))
Eq(F_184(x), F_12(x)*F_185(x))
Eq(F_185(x), F_186(x) + F_188(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_10(x)*F_12(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), 2*F_15(x) + F_184(x) + F_190(x))
Eq(F_190(x), F_12(x)*F_34(x))
Eq(F_191(x), F_12(x)*F_192(x))
Eq(F_192(x), F_193(x) + F_194(x))
Eq(F_193(x), F_10(x) + F_34(x))
Eq(F_194(x), F_195(x) + F_196(x))
Eq(F_195(x), F_15(x) + F_191(x) + F_25(x))
Eq(F_196(x), F_38(x))
Eq(F_197(x), F_198(x) + F_221(x))
Eq(F_198(x), F_15(x) + F_199(x) + F_219(x))
Eq(F_199(x), F_12(x)*F_200(x))
Eq(F_200(x), F_201(x) + F_204(x))
Eq(F_201(x), F_126(x) + F_202(x))
Eq(F_202(x), F_203(x))
Eq(F_203(x), F_12(x)*F_126(x))
Eq(F_204(x), F_198(x) + F_205(x))
Eq(F_205(x), 2*F_15(x) + F_206(x) + F_210(x))
Eq(F_206(x), F_12(x)*F_207(x))
Eq(F_207(x), F_208(x) + F_209(x))
Eq(F_208(x), F_202(x))
Eq(F_209(x), F_205(x))
Eq(F_210(x), F_12(x)*F_211(x))
Eq(F_211(x), F_212(x))
Eq(F_212(x), F_12(x)*F_213(x))
Eq(F_213(x), F_201(x) + F_214(x))
Eq(F_214(x), F_211(x) + F_215(x))
Eq(F_215(x), 2*F_15(x) + F_210(x) + F_216(x))
Eq(F_216(x), F_12(x)*F_217(x))
Eq(F_217(x), F_208(x) + F_218(x))
Eq(F_218(x), F_215(x))
Eq(F_219(x), F_12(x)*F_220(x))
Eq(F_220(x), F_144(x) + F_211(x))
Eq(F_221(x), F_15(x) + F_222(x) + F_246(x) + F_248(x))
Eq(F_222(x), F_12(x)*F_223(x))
Eq(F_223(x), F_224(x) + F_227(x))
Eq(F_224(x), F_129(x) + F_225(x))
Eq(F_225(x), F_226(x))
Eq(F_226(x), F_12(x)*F_129(x))
Eq(F_227(x), F_221(x) + F_228(x))
Eq(F_228(x), 2*F_15(x) + F_229(x) + F_233(x) + F_245(x))
Eq(F_229(x), F_12(x)*F_230(x))
Eq(F_230(x), F_231(x) + F_232(x))
Eq(F_231(x), F_225(x))
Eq(F_232(x), F_228(x))
Eq(F_233(x), F_12(x)*F_234(x))
Eq(F_234(x), F_235(x))
Eq(F_235(x), F_12(x)*F_236(x))
Eq(F_236(x), F_237(x) + F_239(x))
Eq(F_237(x), F_129(x) + F_238(x))
Eq(F_238(x), F_226(x))
Eq(F_239(x), F_234(x) + F_240(x))
Eq(F_240(x), 3*F_15(x) + F_233(x) + F_241(x))
Eq(F_241(x), F_12(x)*F_242(x))
Eq(F_242(x), F_243(x) + F_244(x))
Eq(F_243(x), F_238(x))
Eq(F_244(x), F_240(x))
Eq(F_245(x), 0)
Eq(F_246(x), F_12(x)*F_247(x))
Eq(F_247(x), F_173(x) + F_234(x))
Eq(F_248(x), F_12(x)*F_249(x))
Eq(F_249(x), F_250(x) + F_251(x))
Eq(F_250(x), F_187(x))
Eq(F_251(x), F_252(x))
Eq(F_252(x), 2*F_15(x) + F_190(x) + F_248(x))
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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