0123_0231_0321_1230
Counting sequence:
1, 1, 2, 6, 20, 65, 204, 623, 1864, 5490, 15970, 45991, 131352, 372541, 1050350, 2946270, 8227664, 22886573, 63442404, 175321835, 483156340, 1328165706, 3642763102, 9970372051, 27237676080, 74280376825, 202247293274, 549855298998, 1492856152844, 4047932010905, 10963058884860, 29658382807271, 80151385022752, 216396520554786, 583701126037210, 1573094957449855, 4236085096595784, 11398276283294773, 30647590255876934, 82347918041143950, 221117588035390280, 593365695011725061, 1591340619672044052, 4265378683074486371, 11426601864089393740, 30595123693737551610, 81879053136216852694, 219022190687649924523, 585607699925850083424, 1565081297114514895345, 4181057174492421148850, 11165072787562313620326, 29803687888718488373252, 79527588418965492413681, 212134343288771042949420, 565659641668754457765215, 1507841916461119740256504, 4018073911724080171404498, 10704005895995919589247314, 28506614204108599633808215, 75896221922579843609299320, 202010536754535903047984941, 537540458707492816799219102, 1429997565276432429289467966, 3803207344480809165624008000, 10112503064334519269307230045, 26882182529669316552916880964, 71444807971944609919576335323, 189836651046831483885591693604, 504307610703279574246404528810, 1339429168006529465701459674190, 3556766388612145770892282054531, 9442886496773896464230471390352, 25065156103245672525530079258601, 66520354318627519206297522910730, 176505961368093950471444811907350, 468259920826361130248346123587324, 1242050919717652769016438868748873, 3293961803105880364989197201566044, 8734264265331174561772987582775255, 23156051355301918839607043368330960, 61381121112086222279058141140105346, 162681785553077393444320098084077002, 431100424951996254072150308590513711, 1142233583945341611380122576090536360, 3026006421406469011873944509411924005, 8015389869198956477050900472934649334, 21228569658442633145900598382029436398, 56215934333960750087707229570276483384, 148847672554682805771768253547531071925, 394066785735985426064182685831387083380, 1043143352659723560275988105005110173011, 2760995573856637759492821377600313069052, 7306949605744097144534386971986457939546, 19335539652263923448377032622514577832390, 51159622340878575097064879203833197900635, 135347499930976237757955416829657265815744, 358035442144032544025746638498879427042273, 947012348016464175950982488467531247851874, 2504609601759405922873349529091624186640070, 6623386935308548628175814215570520689907700
Generating function in Maple syntax:
(x^4-x^3+7*x^2-5*x+1)/(x^2-3*x+1)^2
Generating function in latex syntax:
\frac{x^{4}-x^{3}+7 x^{2}-5 x +1}{\left(x^{2}-3 x +1\right)^{2}}
Generating function in sympy syntax:
(x**4 - x**3 + 7*x**2 - 5*x + 1)/(x**2 - 3*x + 1)**2
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)^2*F(x)-x^4+x^3-7*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right)^{2} F \! \left(x \right)-x^{4}+x^{3}-7 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/5*n*(2*(3/2+1/2*5^(1/2))^(-n)*5^(1/2)-2*(3/2-1/2*5^(1/2))^(-n)*5^(1/2)+5*(3/2+1/2*5^(1/2))^(-n)+5*(3/2-1/2*5^(1/2))^(-n)))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{n \left(2 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}-2 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}+5 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}+5 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}\right)}{5} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(n+4) = -a(n)+6*a(n+1)-11*a(n+2)+6*a(n+3), n >= 5
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(n +4\right) = -a \! \left(n \right)+6 a \! \left(n +1\right)-11 a \! \left(n +2\right)+6 a \! \left(n +3\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14963/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[20,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[11,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[362,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[43,x]
F[25,x] = F[26,x]+F[7,x]
F[26,x] = F[22,x]+F[27,x]+F[37,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[33,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[4,x]
F[33,x] = F[17,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[30,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[14,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[4,x]
F[43,x] = F[21,x]+F[44,x]
F[44,x] = F[22,x]+F[243,x]+F[246,x]+F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[57,x]
F[47,x] = F[26,x]+F[48,x]
F[48,x] = F[22,x]+F[49,x]+F[53,x]+F[55,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[30,x]
F[52,x] = F[34,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[33,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[39,x]
F[57,x] = F[44,x]+F[58,x]
F[58,x] = F[125,x]+F[128,x]+F[179,x]+F[22,x]+F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[65,x]
F[61,x] = F[48,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[52,x]
F[65,x] = F[58,x]+F[66,x]
F[66,x] = F[123,x]+F[124,x]+F[22,x]+F[67,x]+F[71,x]+F[72,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[62,x]
F[70,x] = F[66,x]
F[71,x] = 0
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[75,x]
F[75,x] = 3*F[22,x]+F[76,x]+F[91,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[78,x]+F[82,x]
F[78,x] = F[34,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[34,x]
F[82,x] = F[75,x]+F[83,x]
F[83,x] = 3*F[22,x]+F[84,x]+F[88,x]+F[89,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[79,x]
F[87,x] = F[83,x]
F[88,x] = 0
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[75,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[102,x]+F[96,x]
F[96,x] = F[30,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[30,x]
F[101,x] = F[34,x]
F[102,x] = F[103,x]+F[93,x]
F[103,x] = 3*F[22,x]+F[104,x]+F[120,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[106,x]+F[110,x]
F[106,x] = F[107,x]+F[97,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[101,x]
F[110,x] = F[103,x]+F[111,x]
F[111,x] = 3*F[22,x]+F[112,x]+F[116,x]+F[117,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[107,x]
F[115,x] = F[111,x]
F[116,x] = 0
F[117,x] = F[118,x]*F[4,x]
F[118,x] = F[119,x]
F[119,x] = F[75,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[119,x]+F[122,x]
F[122,x] = F[93,x]
F[123,x] = 0
F[124,x] = 0
F[125,x] = F[126,x]*F[4,x]
F[126,x] = F[127,x]+F[74,x]
F[127,x] = F[93,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[130,x]
F[130,x] = F[131,x]+F[75,x]
F[131,x] = 2*F[22,x]+F[132,x]+F[147,x]
F[132,x] = F[133,x]*F[4,x]
F[133,x] = F[134,x]+F[138,x]
F[134,x] = F[135,x]+F[17,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[4,x]
F[137,x] = F[17,x]
F[138,x] = F[131,x]+F[139,x]
F[139,x] = 2*F[22,x]+F[140,x]+F[144,x]+F[145,x]
F[140,x] = F[141,x]*F[4,x]
F[141,x] = F[142,x]+F[143,x]
F[142,x] = F[135,x]
F[143,x] = F[139,x]
F[144,x] = 0
F[145,x] = F[146,x]*F[4,x]
F[146,x] = F[131,x]
F[147,x] = F[148,x]*F[4,x]
F[148,x] = F[149,x]
F[149,x] = F[150,x]
F[150,x] = F[151,x]*F[4,x]
F[151,x] = F[152,x]+F[158,x]
F[152,x] = F[11,x]+F[153,x]
F[153,x] = F[154,x]
F[154,x] = F[155,x]*F[4,x]
F[155,x] = F[156,x]+F[157,x]
F[156,x] = F[11,x]
F[157,x] = F[17,x]
F[158,x] = F[149,x]+F[159,x]
F[159,x] = 2*F[22,x]+F[160,x]+F[176,x]
F[160,x] = F[161,x]*F[4,x]
F[161,x] = F[162,x]+F[166,x]
F[162,x] = F[153,x]+F[163,x]
F[163,x] = F[164,x]
F[164,x] = F[165,x]*F[4,x]
F[165,x] = F[157,x]
F[166,x] = F[159,x]+F[167,x]
F[167,x] = 2*F[22,x]+F[168,x]+F[172,x]+F[173,x]
F[168,x] = F[169,x]*F[4,x]
F[169,x] = F[170,x]+F[171,x]
F[170,x] = F[163,x]
F[171,x] = F[167,x]
F[172,x] = 0
F[173,x] = F[174,x]*F[4,x]
F[174,x] = F[175,x]
F[175,x] = F[131,x]
F[176,x] = F[177,x]*F[4,x]
F[177,x] = F[175,x]+F[178,x]
F[178,x] = F[149,x]
F[179,x] = F[180,x]*F[4,x]
F[180,x] = F[181,x]
F[181,x] = F[182,x]
F[182,x] = 2*F[22,x]+F[183,x]+F[211,x]
F[183,x] = F[184,x]*F[4,x]
F[184,x] = F[185,x]+F[190,x]
F[185,x] = F[186,x]+F[40,x]
F[186,x] = F[187,x]
F[187,x] = F[188,x]*F[4,x]
F[188,x] = F[189,x]
F[189,x] = F[41,x]
F[190,x] = F[182,x]+F[191,x]
F[191,x] = 2*F[22,x]+F[192,x]+F[196,x]+F[197,x]
F[192,x] = F[193,x]*F[4,x]
F[193,x] = F[194,x]+F[195,x]
F[194,x] = F[186,x]
F[195,x] = F[191,x]
F[196,x] = 0
F[197,x] = F[198,x]*F[4,x]
F[198,x] = F[199,x]
F[199,x] = 2*F[22,x]+F[200,x]+F[211,x]
F[200,x] = F[201,x]*F[4,x]
F[201,x] = F[202,x]+F[204,x]
F[202,x] = F[189,x]+F[203,x]
F[203,x] = F[187,x]
F[204,x] = F[199,x]+F[205,x]
F[205,x] = 2*F[22,x]+F[197,x]+F[206,x]+F[210,x]
F[206,x] = F[207,x]*F[4,x]
F[207,x] = F[208,x]+F[209,x]
F[208,x] = F[203,x]
F[209,x] = F[205,x]
F[210,x] = 0
F[211,x] = F[212,x]*F[4,x]
F[212,x] = F[213,x]
F[213,x] = F[214,x]
F[214,x] = F[215,x]*F[4,x]
F[215,x] = F[216,x]+F[222,x]
F[216,x] = F[217,x]+F[4,x]
F[217,x] = F[218,x]
F[218,x] = F[219,x]*F[4,x]
F[219,x] = F[220,x]+F[221,x]
F[220,x] = F[4,x]
F[221,x] = F[189,x]
F[222,x] = F[213,x]+F[223,x]
F[223,x] = 2*F[22,x]+F[224,x]+F[240,x]
F[224,x] = F[225,x]*F[4,x]
F[225,x] = F[226,x]+F[230,x]
F[226,x] = F[217,x]+F[227,x]
F[227,x] = F[228,x]
F[228,x] = F[229,x]*F[4,x]
F[229,x] = F[221,x]
F[230,x] = F[223,x]+F[231,x]
F[231,x] = 2*F[22,x]+F[232,x]+F[236,x]+F[237,x]
F[232,x] = F[233,x]*F[4,x]
F[233,x] = F[234,x]+F[235,x]
F[234,x] = F[227,x]
F[235,x] = F[231,x]
F[236,x] = 0
F[237,x] = F[238,x]*F[4,x]
F[238,x] = F[239,x]
F[239,x] = F[199,x]
F[240,x] = F[241,x]*F[4,x]
F[241,x] = F[239,x]+F[242,x]
F[242,x] = F[213,x]
F[243,x] = F[244,x]*F[4,x]
F[244,x] = F[130,x]+F[245,x]
F[245,x] = F[149,x]+F[93,x]
F[246,x] = F[247,x]*F[4,x]
F[247,x] = F[181,x]+F[248,x]
F[248,x] = F[131,x]+F[249,x]
F[249,x] = F[22,x]+F[250,x]+F[360,x]
F[250,x] = F[251,x]*F[4,x]
F[251,x] = F[252,x]+F[265,x]
F[252,x] = F[15,x]+F[253,x]
F[253,x] = F[22,x]+F[254,x]+F[263,x]
F[254,x] = F[255,x]*F[4,x]
F[255,x] = F[256,x]+F[259,x]
F[256,x] = F[257,x]+F[4,x]
F[257,x] = F[258,x]
F[258,x] = x^2
F[259,x] = F[189,x]+F[260,x]
F[260,x] = F[261,x]
F[261,x] = F[262,x]*F[4,x]
F[262,x] = F[257,x]
F[263,x] = F[264,x]*F[4,x]
F[264,x] = F[15,x]+F[189,x]
F[265,x] = F[249,x]+F[266,x]
F[266,x] = F[22,x]+F[267,x]+F[355,x]+F[358,x]
F[267,x] = F[268,x]*F[4,x]
F[268,x] = F[269,x]+F[279,x]
F[269,x] = F[253,x]+F[270,x]
F[270,x] = F[22,x]+F[271,x]+F[275,x]+F[277,x]
F[271,x] = F[272,x]*F[4,x]
F[272,x] = F[273,x]+F[274,x]
F[273,x] = F[257,x]
F[274,x] = F[260,x]
F[275,x] = F[276,x]*F[4,x]
F[276,x] = F[259,x]
F[277,x] = F[278,x]*F[4,x]
F[278,x] = F[40,x]
F[279,x] = F[266,x]+F[280,x]
F[280,x] = F[22,x]+F[281,x]+F[347,x]+F[350,x]+F[353,x]
F[281,x] = F[282,x]*F[4,x]
F[282,x] = F[283,x]+F[287,x]
F[283,x] = F[270,x]+F[284,x]
F[284,x] = F[285,x]
F[285,x] = F[286,x]*F[4,x]
F[286,x] = F[274,x]
F[287,x] = F[280,x]+F[288,x]
F[288,x] = F[22,x]+F[289,x]+F[293,x]+F[294,x]+F[345,x]+F[346,x]
F[289,x] = F[290,x]*F[4,x]
F[290,x] = F[291,x]+F[292,x]
F[291,x] = F[284,x]
F[292,x] = F[288,x]
F[293,x] = 0
F[294,x] = F[295,x]*F[4,x]
F[295,x] = F[296,x]
F[296,x] = F[297,x]
F[297,x] = 3*F[22,x]+F[298,x]+F[313,x]
F[298,x] = F[299,x]*F[4,x]
F[299,x] = F[300,x]+F[304,x]
F[300,x] = F[260,x]+F[301,x]
F[301,x] = F[302,x]
F[302,x] = F[303,x]*F[4,x]
F[303,x] = F[260,x]
F[304,x] = F[297,x]+F[305,x]
F[305,x] = 3*F[22,x]+F[306,x]+F[310,x]+F[311,x]
F[306,x] = F[307,x]*F[4,x]
F[307,x] = F[308,x]+F[309,x]
F[308,x] = F[301,x]
F[309,x] = F[305,x]
F[310,x] = 0
F[311,x] = F[312,x]*F[4,x]
F[312,x] = F[297,x]
F[313,x] = F[314,x]*F[4,x]
F[314,x] = F[315,x]
F[315,x] = F[316,x]
F[316,x] = F[317,x]*F[4,x]
F[317,x] = F[318,x]+F[324,x]
F[318,x] = F[257,x]+F[319,x]
F[319,x] = F[320,x]
F[320,x] = F[321,x]*F[4,x]
F[321,x] = F[322,x]+F[323,x]
F[322,x] = F[257,x]
F[323,x] = F[260,x]
F[324,x] = F[315,x]+F[325,x]
F[325,x] = 3*F[22,x]+F[326,x]+F[342,x]
F[326,x] = F[327,x]*F[4,x]
F[327,x] = F[328,x]+F[332,x]
F[328,x] = F[319,x]+F[329,x]
F[329,x] = F[330,x]
F[330,x] = F[331,x]*F[4,x]
F[331,x] = F[323,x]
F[332,x] = F[325,x]+F[333,x]
F[333,x] = 3*F[22,x]+F[334,x]+F[338,x]+F[339,x]
F[334,x] = F[335,x]*F[4,x]
F[335,x] = F[336,x]+F[337,x]
F[336,x] = F[329,x]
F[337,x] = F[333,x]
F[338,x] = 0
F[339,x] = F[340,x]*F[4,x]
F[340,x] = F[341,x]
F[341,x] = F[297,x]
F[342,x] = F[343,x]*F[4,x]
F[343,x] = F[341,x]+F[344,x]
F[344,x] = F[315,x]
F[345,x] = 0
F[346,x] = 0
F[347,x] = F[348,x]*F[4,x]
F[348,x] = F[296,x]+F[349,x]
F[349,x] = F[315,x]
F[350,x] = F[351,x]*F[4,x]
F[351,x] = F[352,x]
F[352,x] = F[199,x]+F[297,x]
F[353,x] = F[354,x]*F[4,x]
F[354,x] = F[182,x]
F[355,x] = F[356,x]*F[4,x]
F[356,x] = F[352,x]+F[357,x]
F[357,x] = F[213,x]+F[315,x]
F[358,x] = F[359,x]*F[4,x]
F[359,x] = F[199,x]+F[249,x]
F[360,x] = F[361,x]*F[4,x]
F[361,x] = F[2,x]+F[213,x]
F[362,x] = F[363,x]*F[4,x]
F[363,x] = F[248,x]+F[364,x]
F[364,x] = F[149,x]+F[2,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_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{20}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \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_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{362}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{43}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{7}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{37}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{17}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{21}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{22}\! \left(x \right)+F_{243}\! \left(x \right)+F_{246}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{57}\! \left(x \right)
F_{47}\! \left(x \right) = F_{26}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{22}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{30}\! \left(x \right)
F_{52}\! \left(x \right) = F_{34}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{33}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{39}\! \left(x \right)
F_{57}\! \left(x \right) = F_{44}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{125}\! \left(x \right)+F_{128}\! \left(x \right)+F_{179}\! \left(x \right)+F_{22}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{61}\! \left(x \right) = F_{48}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{52}\! \left(x \right)
F_{65}\! \left(x \right) = F_{58}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{123}\! \left(x \right)+F_{124}\! \left(x \right)+F_{22}\! \left(x \right)+F_{67}\! \left(x \right)+F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \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_{62}\! \left(x \right)
F_{70}\! \left(x \right) = F_{66}\! \left(x \right)
F_{71}\! \left(x \right) = 0
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{76}\! \left(x \right)+F_{91}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{82}\! \left(x \right)
F_{78}\! \left(x \right) = F_{34}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{34}\! \left(x \right)
F_{82}\! \left(x \right) = F_{75}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{84}\! \left(x \right)+F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{79}\! \left(x \right)
F_{87}\! \left(x \right) = F_{83}\! \left(x \right)
F_{88}\! \left(x \right) = 0
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{75}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{102}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{30}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{30}\! \left(x \right)
F_{101}\! \left(x \right) = F_{34}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{93}\! \left(x \right)
F_{103}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{104}\! \left(x \right)+F_{120}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{110}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{97}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{101}\! \left(x \right)
F_{110}\! \left(x \right) = F_{103}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{112}\! \left(x \right)+F_{116}\! \left(x \right)+F_{117}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{107}\! \left(x \right)
F_{115}\! \left(x \right) = F_{111}\! \left(x \right)
F_{116}\! \left(x \right) = 0
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{75}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{119}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{93}\! \left(x \right)
F_{123}\! \left(x \right) = 0
F_{124}\! \left(x \right) = 0
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{4}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{74}\! \left(x \right)
F_{127}\! \left(x \right) = F_{93}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{75}\! \left(x \right)
F_{131}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{132}\! \left(x \right)+F_{147}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{138}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{17}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = F_{17}\! \left(x \right)
F_{138}\! \left(x \right) = F_{131}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{140}\! \left(x \right)+F_{144}\! \left(x \right)+F_{145}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{143}\! \left(x \right)
F_{142}\! \left(x \right) = F_{135}\! \left(x \right)
F_{143}\! \left(x \right) = F_{139}\! \left(x \right)
F_{144}\! \left(x \right) = 0
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{4}\! \left(x \right)
F_{146}\! \left(x \right) = F_{131}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{4}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right) F_{4}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{158}\! \left(x \right)
F_{152}\! \left(x \right) = F_{11}\! \left(x \right)+F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right) F_{4}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{157}\! \left(x \right)
F_{156}\! \left(x \right) = F_{11}\! \left(x \right)
F_{157}\! \left(x \right) = F_{17}\! \left(x \right)
F_{158}\! \left(x \right) = F_{149}\! \left(x \right)+F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{160}\! \left(x \right)+F_{176}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{4}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{166}\! \left(x \right)
F_{162}\! \left(x \right) = F_{153}\! \left(x \right)+F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right) F_{4}\! \left(x \right)
F_{165}\! \left(x \right) = F_{157}\! \left(x \right)
F_{166}\! \left(x \right) = F_{159}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{168}\! \left(x \right)+F_{172}\! \left(x \right)+F_{173}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right) F_{4}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{171}\! \left(x \right)
F_{170}\! \left(x \right) = F_{163}\! \left(x \right)
F_{171}\! \left(x \right) = F_{167}\! \left(x \right)
F_{172}\! \left(x \right) = 0
F_{173}\! \left(x \right) = F_{174}\! \left(x \right) F_{4}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{131}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right) F_{4}\! \left(x \right)
F_{177}\! \left(x \right) = F_{175}\! \left(x \right)+F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{149}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right) F_{4}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{183}\! \left(x \right)+F_{211}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right) F_{4}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{190}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{40}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right) F_{4}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{41}\! \left(x \right)
F_{190}\! \left(x \right) = F_{182}\! \left(x \right)+F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{192}\! \left(x \right)+F_{196}\! \left(x \right)+F_{197}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right) F_{4}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{195}\! \left(x \right)
F_{194}\! \left(x \right) = F_{186}\! \left(x \right)
F_{195}\! \left(x \right) = F_{191}\! \left(x \right)
F_{196}\! \left(x \right) = 0
F_{197}\! \left(x \right) = F_{198}\! \left(x \right) F_{4}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{200}\! \left(x \right)+F_{211}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right) F_{4}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)+F_{204}\! \left(x \right)
F_{202}\! \left(x \right) = F_{189}\! \left(x \right)+F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = F_{187}\! \left(x \right)
F_{204}\! \left(x \right) = F_{199}\! \left(x \right)+F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{197}\! \left(x \right)+F_{206}\! \left(x \right)+F_{210}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right) F_{4}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{209}\! \left(x \right)
F_{208}\! \left(x \right) = F_{203}\! \left(x \right)
F_{209}\! \left(x \right) = F_{205}\! \left(x \right)
F_{210}\! \left(x \right) = 0
F_{211}\! \left(x \right) = F_{212}\! \left(x \right) F_{4}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right) F_{4}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right)+F_{222}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)+F_{4}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right) F_{4}\! \left(x \right)
F_{219}\! \left(x \right) = F_{220}\! \left(x \right)+F_{221}\! \left(x \right)
F_{220}\! \left(x \right) = F_{4}\! \left(x \right)
F_{221}\! \left(x \right) = F_{189}\! \left(x \right)
F_{222}\! \left(x \right) = F_{213}\! \left(x \right)+F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{224}\! \left(x \right)+F_{240}\! \left(x \right)
F_{224}\! \left(x \right) = F_{225}\! \left(x \right) F_{4}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right)+F_{230}\! \left(x \right)
F_{226}\! \left(x \right) = F_{217}\! \left(x \right)+F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right) F_{4}\! \left(x \right)
F_{229}\! \left(x \right) = F_{221}\! \left(x \right)
F_{230}\! \left(x \right) = F_{223}\! \left(x \right)+F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{232}\! \left(x \right)+F_{236}\! \left(x \right)+F_{237}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right) F_{4}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)+F_{235}\! \left(x \right)
F_{234}\! \left(x \right) = F_{227}\! \left(x \right)
F_{235}\! \left(x \right) = F_{231}\! \left(x \right)
F_{236}\! \left(x \right) = 0
F_{237}\! \left(x \right) = F_{238}\! \left(x \right) F_{4}\! \left(x \right)
F_{238}\! \left(x \right) = F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{199}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right) F_{4}\! \left(x \right)
F_{241}\! \left(x \right) = F_{239}\! \left(x \right)+F_{242}\! \left(x \right)
F_{242}\! \left(x \right) = F_{213}\! \left(x \right)
F_{243}\! \left(x \right) = F_{244}\! \left(x \right) F_{4}\! \left(x \right)
F_{244}\! \left(x \right) = F_{130}\! \left(x \right)+F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{149}\! \left(x \right)+F_{93}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right) F_{4}\! \left(x \right)
F_{247}\! \left(x \right) = F_{181}\! \left(x \right)+F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = F_{131}\! \left(x \right)+F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{22}\! \left(x \right)+F_{250}\! \left(x \right)+F_{360}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right) F_{4}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)+F_{265}\! \left(x \right)
F_{252}\! \left(x \right) = F_{15}\! \left(x \right)+F_{253}\! \left(x \right)
F_{253}\! \left(x \right) = F_{22}\! \left(x \right)+F_{254}\! \left(x \right)+F_{263}\! \left(x \right)
F_{254}\! \left(x \right) = F_{255}\! \left(x \right) F_{4}\! \left(x \right)
F_{255}\! \left(x \right) = F_{256}\! \left(x \right)+F_{259}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right)+F_{4}\! \left(x \right)
F_{257}\! \left(x \right) = F_{258}\! \left(x \right)
F_{258}\! \left(x \right) = x^{2}
F_{259}\! \left(x \right) = F_{189}\! \left(x \right)+F_{260}\! \left(x \right)
F_{260}\! \left(x \right) = F_{261}\! \left(x \right)
F_{261}\! \left(x \right) = F_{262}\! \left(x \right) F_{4}\! \left(x \right)
F_{262}\! \left(x \right) = F_{257}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right) F_{4}\! \left(x \right)
F_{264}\! \left(x \right) = F_{15}\! \left(x \right)+F_{189}\! \left(x \right)
F_{265}\! \left(x \right) = F_{249}\! \left(x \right)+F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{22}\! \left(x \right)+F_{267}\! \left(x \right)+F_{355}\! \left(x \right)+F_{358}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right) F_{4}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right)+F_{279}\! \left(x \right)
F_{269}\! \left(x \right) = F_{253}\! \left(x \right)+F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = F_{22}\! \left(x \right)+F_{271}\! \left(x \right)+F_{275}\! \left(x \right)+F_{277}\! \left(x \right)
F_{271}\! \left(x \right) = F_{272}\! \left(x \right) F_{4}\! \left(x \right)
F_{272}\! \left(x \right) = F_{273}\! \left(x \right)+F_{274}\! \left(x \right)
F_{273}\! \left(x \right) = F_{257}\! \left(x \right)
F_{274}\! \left(x \right) = F_{260}\! \left(x \right)
F_{275}\! \left(x \right) = F_{276}\! \left(x \right) F_{4}\! \left(x \right)
F_{276}\! \left(x \right) = F_{259}\! \left(x \right)
F_{277}\! \left(x \right) = F_{278}\! \left(x \right) F_{4}\! \left(x \right)
F_{278}\! \left(x \right) = F_{40}\! \left(x \right)
F_{279}\! \left(x \right) = F_{266}\! \left(x \right)+F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = F_{22}\! \left(x \right)+F_{281}\! \left(x \right)+F_{347}\! \left(x \right)+F_{350}\! \left(x \right)+F_{353}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x \right) F_{4}\! \left(x \right)
F_{282}\! \left(x \right) = F_{283}\! \left(x \right)+F_{287}\! \left(x \right)
F_{283}\! \left(x \right) = F_{270}\! \left(x \right)+F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = F_{285}\! \left(x \right)
F_{285}\! \left(x \right) = F_{286}\! \left(x \right) F_{4}\! \left(x \right)
F_{286}\! \left(x \right) = F_{274}\! \left(x \right)
F_{287}\! \left(x \right) = F_{280}\! \left(x \right)+F_{288}\! \left(x \right)
F_{288}\! \left(x \right) = F_{22}\! \left(x \right)+F_{289}\! \left(x \right)+F_{293}\! \left(x \right)+F_{294}\! \left(x \right)+F_{345}\! \left(x \right)+F_{346}\! \left(x \right)
F_{289}\! \left(x \right) = F_{290}\! \left(x \right) F_{4}\! \left(x \right)
F_{290}\! \left(x \right) = F_{291}\! \left(x \right)+F_{292}\! \left(x \right)
F_{291}\! \left(x \right) = F_{284}\! \left(x \right)
F_{292}\! \left(x \right) = F_{288}\! \left(x \right)
F_{293}\! \left(x \right) = 0
F_{294}\! \left(x \right) = F_{295}\! \left(x \right) F_{4}\! \left(x \right)
F_{295}\! \left(x \right) = F_{296}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right)
F_{297}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{298}\! \left(x \right)+F_{313}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right) F_{4}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)+F_{304}\! \left(x \right)
F_{300}\! \left(x \right) = F_{260}\! \left(x \right)+F_{301}\! \left(x \right)
F_{301}\! \left(x \right) = F_{302}\! \left(x \right)
F_{302}\! \left(x \right) = F_{303}\! \left(x \right) F_{4}\! \left(x \right)
F_{303}\! \left(x \right) = F_{260}\! \left(x \right)
F_{304}\! \left(x \right) = F_{297}\! \left(x \right)+F_{305}\! \left(x \right)
F_{305}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{306}\! \left(x \right)+F_{310}\! \left(x \right)+F_{311}\! \left(x \right)
F_{306}\! \left(x \right) = F_{307}\! \left(x \right) F_{4}\! \left(x \right)
F_{307}\! \left(x \right) = F_{308}\! \left(x \right)+F_{309}\! \left(x \right)
F_{308}\! \left(x \right) = F_{301}\! \left(x \right)
F_{309}\! \left(x \right) = F_{305}\! \left(x \right)
F_{310}\! \left(x \right) = 0
F_{311}\! \left(x \right) = F_{312}\! \left(x \right) F_{4}\! \left(x \right)
F_{312}\! \left(x \right) = F_{297}\! \left(x \right)
F_{313}\! \left(x \right) = F_{314}\! \left(x \right) F_{4}\! \left(x \right)
F_{314}\! \left(x \right) = F_{315}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)
F_{316}\! \left(x \right) = F_{317}\! \left(x \right) F_{4}\! \left(x \right)
F_{317}\! \left(x \right) = F_{318}\! \left(x \right)+F_{324}\! \left(x \right)
F_{318}\! \left(x \right) = F_{257}\! \left(x \right)+F_{319}\! \left(x \right)
F_{319}\! \left(x \right) = F_{320}\! \left(x \right)
F_{320}\! \left(x \right) = F_{321}\! \left(x \right) F_{4}\! \left(x \right)
F_{321}\! \left(x \right) = F_{322}\! \left(x \right)+F_{323}\! \left(x \right)
F_{322}\! \left(x \right) = F_{257}\! \left(x \right)
F_{323}\! \left(x \right) = F_{260}\! \left(x \right)
F_{324}\! \left(x \right) = F_{315}\! \left(x \right)+F_{325}\! \left(x \right)
F_{325}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{326}\! \left(x \right)+F_{342}\! \left(x \right)
F_{326}\! \left(x \right) = F_{327}\! \left(x \right) F_{4}\! \left(x \right)
F_{327}\! \left(x \right) = F_{328}\! \left(x \right)+F_{332}\! \left(x \right)
F_{328}\! \left(x \right) = F_{319}\! \left(x \right)+F_{329}\! \left(x \right)
F_{329}\! \left(x \right) = F_{330}\! \left(x \right)
F_{330}\! \left(x \right) = F_{331}\! \left(x \right) F_{4}\! \left(x \right)
F_{331}\! \left(x \right) = F_{323}\! \left(x \right)
F_{332}\! \left(x \right) = F_{325}\! \left(x \right)+F_{333}\! \left(x \right)
F_{333}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{334}\! \left(x \right)+F_{338}\! \left(x \right)+F_{339}\! \left(x \right)
F_{334}\! \left(x \right) = F_{335}\! \left(x \right) F_{4}\! \left(x \right)
F_{335}\! \left(x \right) = F_{336}\! \left(x \right)+F_{337}\! \left(x \right)
F_{336}\! \left(x \right) = F_{329}\! \left(x \right)
F_{337}\! \left(x \right) = F_{333}\! \left(x \right)
F_{338}\! \left(x \right) = 0
F_{339}\! \left(x \right) = F_{340}\! \left(x \right) F_{4}\! \left(x \right)
F_{340}\! \left(x \right) = F_{341}\! \left(x \right)
F_{341}\! \left(x \right) = F_{297}\! \left(x \right)
F_{342}\! \left(x \right) = F_{343}\! \left(x \right) F_{4}\! \left(x \right)
F_{343}\! \left(x \right) = F_{341}\! \left(x \right)+F_{344}\! \left(x \right)
F_{344}\! \left(x \right) = F_{315}\! \left(x \right)
F_{345}\! \left(x \right) = 0
F_{346}\! \left(x \right) = 0
F_{347}\! \left(x \right) = F_{348}\! \left(x \right) F_{4}\! \left(x \right)
F_{348}\! \left(x \right) = F_{296}\! \left(x \right)+F_{349}\! \left(x \right)
F_{349}\! \left(x \right) = F_{315}\! \left(x \right)
F_{350}\! \left(x \right) = F_{351}\! \left(x \right) F_{4}\! \left(x \right)
F_{351}\! \left(x \right) = F_{352}\! \left(x \right)
F_{352}\! \left(x \right) = F_{199}\! \left(x \right)+F_{297}\! \left(x \right)
F_{353}\! \left(x \right) = F_{354}\! \left(x \right) F_{4}\! \left(x \right)
F_{354}\! \left(x \right) = F_{182}\! \left(x \right)
F_{355}\! \left(x \right) = F_{356}\! \left(x \right) F_{4}\! \left(x \right)
F_{356}\! \left(x \right) = F_{352}\! \left(x \right)+F_{357}\! \left(x \right)
F_{357}\! \left(x \right) = F_{213}\! \left(x \right)+F_{315}\! \left(x \right)
F_{358}\! \left(x \right) = F_{359}\! \left(x \right) F_{4}\! \left(x \right)
F_{359}\! \left(x \right) = F_{199}\! \left(x \right)+F_{249}\! \left(x \right)
F_{360}\! \left(x \right) = F_{361}\! \left(x \right) F_{4}\! \left(x \right)
F_{361}\! \left(x \right) = F_{2}\! \left(x \right)+F_{213}\! \left(x \right)
F_{362}\! \left(x \right) = F_{363}\! \left(x \right) F_{4}\! \left(x \right)
F_{363}\! \left(x \right) = F_{248}\! \left(x \right)+F_{364}\! \left(x \right)
F_{364}\! \left(x \right) = F_{149}\! \left(x \right)+F_{2}\! \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_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_20(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_11(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_362(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_43(x))
Eq(F_25(x), F_26(x) + F_7(x))
Eq(F_26(x), F_22(x) + F_27(x) + F_37(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_33(x))
Eq(F_29(x), F_11(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_4(x))
Eq(F_33(x), F_17(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_30(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_14(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_4(x))
Eq(F_43(x), F_21(x) + F_44(x))
Eq(F_44(x), F_22(x) + F_243(x) + F_246(x) + F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_57(x))
Eq(F_47(x), F_26(x) + F_48(x))
Eq(F_48(x), F_22(x) + F_49(x) + F_53(x) + F_55(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_30(x))
Eq(F_52(x), F_34(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_33(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_39(x))
Eq(F_57(x), F_44(x) + F_58(x))
Eq(F_58(x), F_125(x) + F_128(x) + F_179(x) + F_22(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_65(x))
Eq(F_61(x), F_48(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_52(x))
Eq(F_65(x), F_58(x) + F_66(x))
Eq(F_66(x), F_123(x) + F_124(x) + F_22(x) + F_67(x) + F_71(x) + F_72(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_62(x))
Eq(F_70(x), F_66(x))
Eq(F_71(x), 0)
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), 3*F_22(x) + F_76(x) + F_91(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_82(x))
Eq(F_78(x), F_34(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_34(x))
Eq(F_82(x), F_75(x) + F_83(x))
Eq(F_83(x), 3*F_22(x) + F_84(x) + F_88(x) + F_89(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_79(x))
Eq(F_87(x), F_83(x))
Eq(F_88(x), 0)
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_75(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_102(x) + F_96(x))
Eq(F_96(x), F_30(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_30(x))
Eq(F_101(x), F_34(x))
Eq(F_102(x), F_103(x) + F_93(x))
Eq(F_103(x), F_104(x) + F_120(x) + 3*F_22(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_106(x) + F_110(x))
Eq(F_106(x), F_107(x) + F_97(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_101(x))
Eq(F_110(x), F_103(x) + F_111(x))
Eq(F_111(x), F_112(x) + F_116(x) + F_117(x) + 3*F_22(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_107(x))
Eq(F_115(x), F_111(x))
Eq(F_116(x), 0)
Eq(F_117(x), F_118(x)*F_4(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_75(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_119(x) + F_122(x))
Eq(F_122(x), F_93(x))
Eq(F_123(x), 0)
Eq(F_124(x), 0)
Eq(F_125(x), F_126(x)*F_4(x))
Eq(F_126(x), F_127(x) + F_74(x))
Eq(F_127(x), F_93(x))
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x) + F_75(x))
Eq(F_131(x), F_132(x) + F_147(x) + 2*F_22(x))
Eq(F_132(x), F_133(x)*F_4(x))
Eq(F_133(x), F_134(x) + F_138(x))
Eq(F_134(x), F_135(x) + F_17(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_17(x))
Eq(F_138(x), F_131(x) + F_139(x))
Eq(F_139(x), F_140(x) + F_144(x) + F_145(x) + 2*F_22(x))
Eq(F_140(x), F_141(x)*F_4(x))
Eq(F_141(x), F_142(x) + F_143(x))
Eq(F_142(x), F_135(x))
Eq(F_143(x), F_139(x))
Eq(F_144(x), 0)
Eq(F_145(x), F_146(x)*F_4(x))
Eq(F_146(x), F_131(x))
Eq(F_147(x), F_148(x)*F_4(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_151(x)*F_4(x))
Eq(F_151(x), F_152(x) + F_158(x))
Eq(F_152(x), F_11(x) + F_153(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_155(x)*F_4(x))
Eq(F_155(x), F_156(x) + F_157(x))
Eq(F_156(x), F_11(x))
Eq(F_157(x), F_17(x))
Eq(F_158(x), F_149(x) + F_159(x))
Eq(F_159(x), F_160(x) + F_176(x) + 2*F_22(x))
Eq(F_160(x), F_161(x)*F_4(x))
Eq(F_161(x), F_162(x) + F_166(x))
Eq(F_162(x), F_153(x) + F_163(x))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_165(x)*F_4(x))
Eq(F_165(x), F_157(x))
Eq(F_166(x), F_159(x) + F_167(x))
Eq(F_167(x), F_168(x) + F_172(x) + F_173(x) + 2*F_22(x))
Eq(F_168(x), F_169(x)*F_4(x))
Eq(F_169(x), F_170(x) + F_171(x))
Eq(F_170(x), F_163(x))
Eq(F_171(x), F_167(x))
Eq(F_172(x), 0)
Eq(F_173(x), F_174(x)*F_4(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_131(x))
Eq(F_176(x), F_177(x)*F_4(x))
Eq(F_177(x), F_175(x) + F_178(x))
Eq(F_178(x), F_149(x))
Eq(F_179(x), F_180(x)*F_4(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_182(x))
Eq(F_182(x), F_183(x) + F_211(x) + 2*F_22(x))
Eq(F_183(x), F_184(x)*F_4(x))
Eq(F_184(x), F_185(x) + F_190(x))
Eq(F_185(x), F_186(x) + F_40(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_188(x)*F_4(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_41(x))
Eq(F_190(x), F_182(x) + F_191(x))
Eq(F_191(x), F_192(x) + F_196(x) + F_197(x) + 2*F_22(x))
Eq(F_192(x), F_193(x)*F_4(x))
Eq(F_193(x), F_194(x) + F_195(x))
Eq(F_194(x), F_186(x))
Eq(F_195(x), F_191(x))
Eq(F_196(x), 0)
Eq(F_197(x), F_198(x)*F_4(x))
Eq(F_198(x), F_199(x))
Eq(F_199(x), F_200(x) + F_211(x) + 2*F_22(x))
Eq(F_200(x), F_201(x)*F_4(x))
Eq(F_201(x), F_202(x) + F_204(x))
Eq(F_202(x), F_189(x) + F_203(x))
Eq(F_203(x), F_187(x))
Eq(F_204(x), F_199(x) + F_205(x))
Eq(F_205(x), F_197(x) + F_206(x) + F_210(x) + 2*F_22(x))
Eq(F_206(x), F_207(x)*F_4(x))
Eq(F_207(x), F_208(x) + F_209(x))
Eq(F_208(x), F_203(x))
Eq(F_209(x), F_205(x))
Eq(F_210(x), 0)
Eq(F_211(x), F_212(x)*F_4(x))
Eq(F_212(x), F_213(x))
Eq(F_213(x), F_214(x))
Eq(F_214(x), F_215(x)*F_4(x))
Eq(F_215(x), F_216(x) + F_222(x))
Eq(F_216(x), F_217(x) + F_4(x))
Eq(F_217(x), F_218(x))
Eq(F_218(x), F_219(x)*F_4(x))
Eq(F_219(x), F_220(x) + F_221(x))
Eq(F_220(x), F_4(x))
Eq(F_221(x), F_189(x))
Eq(F_222(x), F_213(x) + F_223(x))
Eq(F_223(x), 2*F_22(x) + F_224(x) + F_240(x))
Eq(F_224(x), F_225(x)*F_4(x))
Eq(F_225(x), F_226(x) + F_230(x))
Eq(F_226(x), F_217(x) + F_227(x))
Eq(F_227(x), F_228(x))
Eq(F_228(x), F_229(x)*F_4(x))
Eq(F_229(x), F_221(x))
Eq(F_230(x), F_223(x) + F_231(x))
Eq(F_231(x), 2*F_22(x) + F_232(x) + F_236(x) + F_237(x))
Eq(F_232(x), F_233(x)*F_4(x))
Eq(F_233(x), F_234(x) + F_235(x))
Eq(F_234(x), F_227(x))
Eq(F_235(x), F_231(x))
Eq(F_236(x), 0)
Eq(F_237(x), F_238(x)*F_4(x))
Eq(F_238(x), F_239(x))
Eq(F_239(x), F_199(x))
Eq(F_240(x), F_241(x)*F_4(x))
Eq(F_241(x), F_239(x) + F_242(x))
Eq(F_242(x), F_213(x))
Eq(F_243(x), F_244(x)*F_4(x))
Eq(F_244(x), F_130(x) + F_245(x))
Eq(F_245(x), F_149(x) + F_93(x))
Eq(F_246(x), F_247(x)*F_4(x))
Eq(F_247(x), F_181(x) + F_248(x))
Eq(F_248(x), F_131(x) + F_249(x))
Eq(F_249(x), F_22(x) + F_250(x) + F_360(x))
Eq(F_250(x), F_251(x)*F_4(x))
Eq(F_251(x), F_252(x) + F_265(x))
Eq(F_252(x), F_15(x) + F_253(x))
Eq(F_253(x), F_22(x) + F_254(x) + F_263(x))
Eq(F_254(x), F_255(x)*F_4(x))
Eq(F_255(x), F_256(x) + F_259(x))
Eq(F_256(x), F_257(x) + F_4(x))
Eq(F_257(x), F_258(x))
Eq(F_258(x), x**2)
Eq(F_259(x), F_189(x) + F_260(x))
Eq(F_260(x), F_261(x))
Eq(F_261(x), F_262(x)*F_4(x))
Eq(F_262(x), F_257(x))
Eq(F_263(x), F_264(x)*F_4(x))
Eq(F_264(x), F_15(x) + F_189(x))
Eq(F_265(x), F_249(x) + F_266(x))
Eq(F_266(x), F_22(x) + F_267(x) + F_355(x) + F_358(x))
Eq(F_267(x), F_268(x)*F_4(x))
Eq(F_268(x), F_269(x) + F_279(x))
Eq(F_269(x), F_253(x) + F_270(x))
Eq(F_270(x), F_22(x) + F_271(x) + F_275(x) + F_277(x))
Eq(F_271(x), F_272(x)*F_4(x))
Eq(F_272(x), F_273(x) + F_274(x))
Eq(F_273(x), F_257(x))
Eq(F_274(x), F_260(x))
Eq(F_275(x), F_276(x)*F_4(x))
Eq(F_276(x), F_259(x))
Eq(F_277(x), F_278(x)*F_4(x))
Eq(F_278(x), F_40(x))
Eq(F_279(x), F_266(x) + F_280(x))
Eq(F_280(x), F_22(x) + F_281(x) + F_347(x) + F_350(x) + F_353(x))
Eq(F_281(x), F_282(x)*F_4(x))
Eq(F_282(x), F_283(x) + F_287(x))
Eq(F_283(x), F_270(x) + F_284(x))
Eq(F_284(x), F_285(x))
Eq(F_285(x), F_286(x)*F_4(x))
Eq(F_286(x), F_274(x))
Eq(F_287(x), F_280(x) + F_288(x))
Eq(F_288(x), F_22(x) + F_289(x) + F_293(x) + F_294(x) + F_345(x) + F_346(x))
Eq(F_289(x), F_290(x)*F_4(x))
Eq(F_290(x), F_291(x) + F_292(x))
Eq(F_291(x), F_284(x))
Eq(F_292(x), F_288(x))
Eq(F_293(x), 0)
Eq(F_294(x), F_295(x)*F_4(x))
Eq(F_295(x), F_296(x))
Eq(F_296(x), F_297(x))
Eq(F_297(x), 3*F_22(x) + F_298(x) + F_313(x))
Eq(F_298(x), F_299(x)*F_4(x))
Eq(F_299(x), F_300(x) + F_304(x))
Eq(F_300(x), F_260(x) + F_301(x))
Eq(F_301(x), F_302(x))
Eq(F_302(x), F_303(x)*F_4(x))
Eq(F_303(x), F_260(x))
Eq(F_304(x), F_297(x) + F_305(x))
Eq(F_305(x), 3*F_22(x) + F_306(x) + F_310(x) + F_311(x))
Eq(F_306(x), F_307(x)*F_4(x))
Eq(F_307(x), F_308(x) + F_309(x))
Eq(F_308(x), F_301(x))
Eq(F_309(x), F_305(x))
Eq(F_310(x), 0)
Eq(F_311(x), F_312(x)*F_4(x))
Eq(F_312(x), F_297(x))
Eq(F_313(x), F_314(x)*F_4(x))
Eq(F_314(x), F_315(x))
Eq(F_315(x), F_316(x))
Eq(F_316(x), F_317(x)*F_4(x))
Eq(F_317(x), F_318(x) + F_324(x))
Eq(F_318(x), F_257(x) + F_319(x))
Eq(F_319(x), F_320(x))
Eq(F_320(x), F_321(x)*F_4(x))
Eq(F_321(x), F_322(x) + F_323(x))
Eq(F_322(x), F_257(x))
Eq(F_323(x), F_260(x))
Eq(F_324(x), F_315(x) + F_325(x))
Eq(F_325(x), 3*F_22(x) + F_326(x) + F_342(x))
Eq(F_326(x), F_327(x)*F_4(x))
Eq(F_327(x), F_328(x) + F_332(x))
Eq(F_328(x), F_319(x) + F_329(x))
Eq(F_329(x), F_330(x))
Eq(F_330(x), F_331(x)*F_4(x))
Eq(F_331(x), F_323(x))
Eq(F_332(x), F_325(x) + F_333(x))
Eq(F_333(x), 3*F_22(x) + F_334(x) + F_338(x) + F_339(x))
Eq(F_334(x), F_335(x)*F_4(x))
Eq(F_335(x), F_336(x) + F_337(x))
Eq(F_336(x), F_329(x))
Eq(F_337(x), F_333(x))
Eq(F_338(x), 0)
Eq(F_339(x), F_340(x)*F_4(x))
Eq(F_340(x), F_341(x))
Eq(F_341(x), F_297(x))
Eq(F_342(x), F_343(x)*F_4(x))
Eq(F_343(x), F_341(x) + F_344(x))
Eq(F_344(x), F_315(x))
Eq(F_345(x), 0)
Eq(F_346(x), 0)
Eq(F_347(x), F_348(x)*F_4(x))
Eq(F_348(x), F_296(x) + F_349(x))
Eq(F_349(x), F_315(x))
Eq(F_350(x), F_351(x)*F_4(x))
Eq(F_351(x), F_352(x))
Eq(F_352(x), F_199(x) + F_297(x))
Eq(F_353(x), F_354(x)*F_4(x))
Eq(F_354(x), F_182(x))
Eq(F_355(x), F_356(x)*F_4(x))
Eq(F_356(x), F_352(x) + F_357(x))
Eq(F_357(x), F_213(x) + F_315(x))
Eq(F_358(x), F_359(x)*F_4(x))
Eq(F_359(x), F_199(x) + F_249(x))
Eq(F_360(x), F_361(x)*F_4(x))
Eq(F_361(x), F_2(x) + F_213(x))
Eq(F_362(x), F_363(x)*F_4(x))
Eq(F_363(x), F_248(x) + F_364(x))
Eq(F_364(x), F_149(x) + F_2(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 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, 1, 2, 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": [0, 3, 2, 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": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 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": [0, 3, 2, 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_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"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]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], 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