0123_1230_1320_3021
Counting sequence:
1, 1, 2, 6, 20, 61, 155, 345, 724, 1483, 3017, 6145, 12566, 25803, 53155, 109729, 226760, 468763, 968861, 2001489, 4131898, 8523355, 17567927, 36180817, 74454572, 153098571, 314580145, 645931105, 1325409374, 2717919403, 5570047307, 11408519745, 23353898896, 47781526843, 97710523205, 199715998129, 408021913730, 833223677883, 1700807073631, 3470333601649, 7078106132468, 14431090145515, 29411936076377, 59923383749697, 122045790721702, 248489627918731, 505775348821235, 1029142883645665, 2093470139336024, 4257309022802523, 8655355533909997, 17592186044476945, 35747322042318026, 72620543991417883, 147492887796456455, 299489375220214929, 607985949695098300, 1233986297899601803, 2504001392818086401, 5080060379674015009, 10304235947423795438, 20896702270999207275, 42369865294301737627, 85892652093210216577, 174091147195634016032, 352793980409695303291, 714811332856245259925, 1448069409786199943025, 2933032307719818854674, 5939851591734475774843, 12027277136058627815087, 24349702177296608301745, 49289700164951922093956, 99759991950621255322923, 201881167142677333076905, 408484700768224311184129, 826414134502187912604470, 1671717734935854405864523, 3381214401734665973231171, 6837986667195246269665569, 13827089061842321185944808, 27956409578588299665332635, 56517282066983913917775677, 114243489953582457010005457, 230904831546394172369161562, 466645366371246861436876251, 942962139299410756271120215, 1905267091712655579337247185, 3849219809652979292264789324, 7775810871761294851710460363, 15706364248433262237782986577, 31722213506687869544290418145, 64063397033018429226030050686, 129364734105322238726958865963, 261205348289215238003715608555, 527362456735571997107027329729, 1064628433785427036413247256240, 2149063908199420157224880090043, 4337741897655972483246531731941, 8754711957826209304086606977329, 17667880240680947283360301404578
Generating function in Maple syntax:
(12*x^10-34*x^9+18*x^8+21*x^7-11*x^6-10*x^5+21*x^4-28*x^3+20*x^2-7*x+1)/(2*x-1)^2/(x-1)^4
Generating function in latex syntax:
\frac{12 x^{10}-34 x^{9}+18 x^{8}+21 x^{7}-11 x^{6}-10 x^{5}+21 x^{4}-28 x^{3}+20 x^{2}-7 x +1}{\left(2 x -1\right)^{2} \left(x -1\right)^{4}}
Generating function in sympy syntax:
(12*x**10 - 34*x**9 + 18*x**8 + 21*x**7 - 11*x**6 - 10*x**5 + 21*x**4 - 28*x**3 + 20*x**2 - 7*x + 1)/((x - 1)**4*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
-(2*x-1)^2*(x-1)^4*F(x)+12*x^10-34*x^9+18*x^8+21*x^7-11*x^6-10*x^5+21*x^4-28*x^3+20*x^2-7*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right)^{2} \left(x -1\right)^{4} F \! \left(x \right)+12 x^{10}-34 x^{9}+18 x^{8}+21 x^{7}-11 x^{6}-10 x^{5}+21 x^{4}-28 x^{3}+20 x^{2}-7 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,n = 3,6,n = 4,20,1/16*(2*n+23)*2^n+1/2*n^3-2*n^2-7/2*n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ 6 & n =3 \\ 20 & n =4 \\ \frac{\left(2 n +23\right) 2^{n}}{16}+\frac{n^{3}}{2}-2 n^{2}-\frac{7 n}{2} & \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(5) = 61
a(6) = 155
a(7) = 345
a(8) = 724
a(9) = 1483
a(10) = 3017
a(n+2) = 1/2*n^3-5*n^2-4*a(n)+4*a(n+1)+9/2*n+9, n >= 11
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 61
a \! \left(6\right) = 155
a \! \left(7\right) = 345
a \! \left(8\right) = 724
a \! \left(9\right) = 1483
a \! \left(10\right) = 3017
a \! \left(n +2\right) = \frac{n^{3}}{2}-5 n^{2}-4 a \! \left(n \right)+4 a \! \left(n +1\right)+\frac{9 n}{2}+9, \quad n \geq 11
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15188/
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[47,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[26,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[4,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]+F[25,x]
F[20,x] = 0
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[4,x]
F[24,x] = F[19,x]
F[25,x] = F[14,x]*F[4,x]
F[26,x] = F[20,x]+F[27,x]+F[44,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[26,x]+F[34,x]
F[34,x] = 2*F[20,x]+F[35,x]+F[39,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[30,x]
F[38,x] = F[34,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[23,x]+F[43,x]
F[43,x] = F[41,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[14,x]+F[46,x]
F[46,x] = F[41,x]
F[47,x] = F[48,x]+F[82,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[54,x]
F[51,x] = F[1,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[17,x]*F[4,x]
F[54,x] = F[48,x]+F[55,x]
F[55,x] = F[20,x]+F[56,x]+F[80,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[61,x]
F[58,x] = F[52,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[23,x]*F[4,x]
F[61,x] = F[55,x]+F[62,x]
F[62,x] = 2*F[20,x]+F[63,x]+F[67,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[59,x]
F[66,x] = F[62,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]+F[74,x]
F[72,x] = F[4,x]+F[73,x]
F[73,x] = F[60,x]
F[74,x] = F[69,x]+F[75,x]
F[75,x] = 2*F[20,x]+F[67,x]+F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[73,x]
F[79,x] = F[75,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[48,x]+F[69,x]
F[82,x] = F[171,x]+F[20,x]+F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[99,x]
F[85,x] = F[7,x]+F[86,x]
F[86,x] = F[20,x]+F[87,x]+F[88,x]
F[87,x] = F[29,x]*F[4,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]+F[94,x]
F[90,x] = F[52,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[11,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[60,x]
F[96,x] = F[97,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[30,x]
F[99,x] = F[100,x]+F[82,x]
F[100,x] = F[101,x]+F[134,x]+F[148,x]+F[20,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]+F[108,x]
F[103,x] = F[104,x]+F[86,x]
F[104,x] = 2*F[20,x]+F[105,x]+F[106,x]
F[105,x] = F[37,x]*F[4,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[59,x]
F[108,x] = F[100,x]+F[109,x]
F[109,x] = 2*F[20,x]+F[110,x]+F[114,x]+F[129,x]
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[104,x]
F[113,x] = F[109,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[4,x]
F[118,x] = F[119,x]+F[121,x]
F[119,x] = F[120,x]+F[30,x]
F[120,x] = F[97,x]
F[121,x] = F[116,x]+F[122,x]
F[122,x] = 3*F[20,x]+F[123,x]+F[127,x]
F[123,x] = F[124,x]*F[4,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[120,x]
F[126,x] = F[122,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[116,x]
F[129,x] = F[130,x]*F[4,x]
F[130,x] = F[131,x]
F[131,x] = F[132,x]*F[4,x]
F[132,x] = F[133,x]+F[65,x]
F[133,x] = F[131,x]
F[134,x] = F[135,x]*F[4,x]
F[135,x] = F[116,x]+F[136,x]
F[136,x] = F[137,x]
F[137,x] = F[138,x]*F[4,x]
F[138,x] = F[139,x]+F[140,x]
F[139,x] = F[11,x]+F[91,x]
F[140,x] = F[136,x]+F[141,x]
F[141,x] = 2*F[20,x]+F[142,x]+F[146,x]
F[142,x] = F[143,x]*F[4,x]
F[143,x] = F[144,x]+F[145,x]
F[144,x] = F[91,x]
F[145,x] = F[141,x]
F[146,x] = F[147,x]*F[4,x]
F[147,x] = F[136,x]
F[148,x] = F[149,x]*F[4,x]
F[149,x] = F[150,x]+F[163,x]
F[150,x] = F[151,x]+F[159,x]
F[151,x] = F[152,x]
F[152,x] = F[153,x]*F[4,x]
F[153,x] = F[154,x]+F[58,x]
F[154,x] = F[151,x]+F[155,x]
F[155,x] = 2*F[20,x]+F[156,x]+F[67,x]
F[156,x] = F[157,x]*F[4,x]
F[157,x] = F[158,x]+F[65,x]
F[158,x] = F[155,x]
F[159,x] = F[160,x]
F[160,x] = F[161,x]*F[4,x]
F[161,x] = F[144,x]+F[162,x]
F[162,x] = F[159,x]
F[163,x] = F[164,x]+F[165,x]
F[164,x] = F[131,x]
F[165,x] = F[166,x]
F[166,x] = F[167,x]*F[4,x]
F[167,x] = F[168,x]+F[170,x]
F[168,x] = F[169,x]
F[169,x] = F[97,x]
F[170,x] = F[166,x]
F[171,x] = F[172,x]*F[4,x]
F[172,x] = F[173,x]+F[174,x]
F[173,x] = F[136,x]+F[48,x]
F[174,x] = F[175,x]+F[176,x]
F[175,x] = F[152,x]
F[176,x] = F[177,x]
F[177,x] = F[178,x]*F[4,x]
F[178,x] = F[179,x]+F[184,x]
F[179,x] = F[169,x]+F[180,x]
F[180,x] = F[181,x]+F[20,x]+F[87,x]
F[181,x] = F[182,x]*F[4,x]
F[182,x] = F[183,x]+F[52,x]
F[183,x] = F[60,x]
F[184,x] = F[185,x]+F[186,x]
F[185,x] = F[177,x]
F[186,x] = 3*F[20,x]+F[127,x]+F[187,x]
F[187,x] = F[188,x]*F[4,x]
F[188,x] = F[168,x]+F[189,x]
F[189,x] = F[186,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_{47}\! \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_{13}\! \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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{26}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)+F_{44}\! \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_{26}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{35}\! \left(x \right)+F_{39}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{30}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \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_{23}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{41}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{82}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \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_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{1}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{54}\! \left(x \right) = F_{48}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right)+F_{56}\! \left(x \right)+F_{80}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = F_{52}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{61}\! \left(x \right) = F_{55}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{63}\! \left(x \right)+F_{67}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{59}\! \left(x \right)
F_{66}\! \left(x \right) = F_{62}\! \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_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{60}\! \left(x \right)
F_{74}\! \left(x \right) = F_{69}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{67}\! \left(x \right)+F_{76}\! \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_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{73}\! \left(x \right)
F_{79}\! \left(x \right) = F_{75}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{48}\! \left(x \right)+F_{69}\! \left(x \right)
F_{82}\! \left(x \right) = F_{171}\! \left(x \right)+F_{20}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{99}\! \left(x \right)
F_{85}\! \left(x \right) = F_{7}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{20}\! \left(x \right)+F_{87}\! \left(x \right)+F_{88}\! \left(x \right)
F_{87}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{94}\! \left(x \right)
F_{90}\! \left(x \right) = F_{52}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{11}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{60}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{30}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{82}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{134}\! \left(x \right)+F_{148}\! \left(x \right)+F_{20}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{108}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{86}\! \left(x \right)
F_{104}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{59}\! \left(x \right)
F_{108}\! \left(x \right) = F_{100}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{110}\! \left(x \right)+F_{114}\! \left(x \right)+F_{129}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{104}\! \left(x \right)
F_{113}\! \left(x \right) = F_{109}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
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_{121}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{30}\! \left(x \right)
F_{120}\! \left(x \right) = F_{97}\! \left(x \right)
F_{121}\! \left(x \right) = F_{116}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = 3 F_{20}\! \left(x \right)+F_{123}\! \left(x \right)+F_{127}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{4}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{126}\! \left(x \right)
F_{125}\! \left(x \right) = F_{120}\! \left(x \right)
F_{126}\! \left(x \right) = F_{122}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = F_{116}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{65}\! \left(x \right)
F_{133}\! \left(x \right) = F_{131}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{4}\! \left(x \right)
F_{135}\! \left(x \right) = F_{116}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{4}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{140}\! \left(x \right)
F_{139}\! \left(x \right) = F_{11}\! \left(x \right)+F_{91}\! \left(x \right)
F_{140}\! \left(x \right) = F_{136}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{142}\! \left(x \right)+F_{146}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{145}\! \left(x \right)
F_{144}\! \left(x \right) = F_{91}\! \left(x \right)
F_{145}\! \left(x \right) = F_{141}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right) F_{4}\! \left(x \right)
F_{147}\! \left(x \right) = F_{136}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{4}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{163}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{159}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right) F_{4}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{58}\! \left(x \right)
F_{154}\! \left(x \right) = F_{151}\! \left(x \right)+F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{156}\! \left(x \right)+F_{67}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right) F_{4}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{65}\! \left(x \right)
F_{158}\! \left(x \right) = F_{155}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{4}\! \left(x \right)
F_{161}\! \left(x \right) = F_{144}\! \left(x \right)+F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{159}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)+F_{165}\! \left(x \right)
F_{164}\! \left(x \right) = F_{131}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right) F_{4}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{170}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{97}\! \left(x \right)
F_{170}\! \left(x \right) = F_{166}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right) F_{4}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{174}\! \left(x \right)
F_{173}\! \left(x \right) = F_{136}\! \left(x \right)+F_{48}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{176}\! \left(x \right)
F_{175}\! \left(x \right) = F_{152}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right) F_{4}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)+F_{184}\! \left(x \right)
F_{179}\! \left(x \right) = F_{169}\! \left(x \right)+F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{20}\! \left(x \right)+F_{87}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right) F_{4}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)+F_{52}\! \left(x \right)
F_{183}\! \left(x \right) = F_{60}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{186}\! \left(x \right)
F_{185}\! \left(x \right) = F_{177}\! \left(x \right)
F_{186}\! \left(x \right) = 3 F_{20}\! \left(x \right)+F_{127}\! \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_{168}\! \left(x \right)+F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{186}\! \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_47(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_26(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_4(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_25(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_4(x))
Eq(F_24(x), F_19(x))
Eq(F_25(x), F_14(x)*F_4(x))
Eq(F_26(x), F_20(x) + F_27(x) + F_44(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_26(x) + F_34(x))
Eq(F_34(x), 2*F_20(x) + F_35(x) + F_39(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_30(x))
Eq(F_38(x), F_34(x))
Eq(F_39(x), F_4(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_23(x) + F_43(x))
Eq(F_43(x), F_41(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_14(x) + F_46(x))
Eq(F_46(x), F_41(x))
Eq(F_47(x), F_48(x) + F_82(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_54(x))
Eq(F_51(x), F_1(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_17(x)*F_4(x))
Eq(F_54(x), F_48(x) + F_55(x))
Eq(F_55(x), F_20(x) + F_56(x) + F_80(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_61(x))
Eq(F_58(x), F_52(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_23(x)*F_4(x))
Eq(F_61(x), F_55(x) + F_62(x))
Eq(F_62(x), 2*F_20(x) + F_63(x) + F_67(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_59(x))
Eq(F_66(x), F_62(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_74(x))
Eq(F_72(x), F_4(x) + F_73(x))
Eq(F_73(x), F_60(x))
Eq(F_74(x), F_69(x) + F_75(x))
Eq(F_75(x), 2*F_20(x) + F_67(x) + F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_73(x))
Eq(F_79(x), F_75(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_48(x) + F_69(x))
Eq(F_82(x), F_171(x) + F_20(x) + F_83(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_99(x))
Eq(F_85(x), F_7(x) + F_86(x))
Eq(F_86(x), F_20(x) + F_87(x) + F_88(x))
Eq(F_87(x), F_29(x)*F_4(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_94(x))
Eq(F_90(x), F_52(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_11(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_60(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_30(x))
Eq(F_99(x), F_100(x) + F_82(x))
Eq(F_100(x), F_101(x) + F_134(x) + F_148(x) + F_20(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x) + F_108(x))
Eq(F_103(x), F_104(x) + F_86(x))
Eq(F_104(x), F_105(x) + F_106(x) + 2*F_20(x))
Eq(F_105(x), F_37(x)*F_4(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_59(x))
Eq(F_108(x), F_100(x) + F_109(x))
Eq(F_109(x), F_110(x) + F_114(x) + F_129(x) + 2*F_20(x))
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_104(x))
Eq(F_113(x), F_109(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_4(x))
Eq(F_118(x), F_119(x) + F_121(x))
Eq(F_119(x), F_120(x) + F_30(x))
Eq(F_120(x), F_97(x))
Eq(F_121(x), F_116(x) + F_122(x))
Eq(F_122(x), F_123(x) + F_127(x) + 3*F_20(x))
Eq(F_123(x), F_124(x)*F_4(x))
Eq(F_124(x), F_125(x) + F_126(x))
Eq(F_125(x), F_120(x))
Eq(F_126(x), F_122(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_116(x))
Eq(F_129(x), F_130(x)*F_4(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_132(x)*F_4(x))
Eq(F_132(x), F_133(x) + F_65(x))
Eq(F_133(x), F_131(x))
Eq(F_134(x), F_135(x)*F_4(x))
Eq(F_135(x), F_116(x) + F_136(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_138(x)*F_4(x))
Eq(F_138(x), F_139(x) + F_140(x))
Eq(F_139(x), F_11(x) + F_91(x))
Eq(F_140(x), F_136(x) + F_141(x))
Eq(F_141(x), F_142(x) + F_146(x) + 2*F_20(x))
Eq(F_142(x), F_143(x)*F_4(x))
Eq(F_143(x), F_144(x) + F_145(x))
Eq(F_144(x), F_91(x))
Eq(F_145(x), F_141(x))
Eq(F_146(x), F_147(x)*F_4(x))
Eq(F_147(x), F_136(x))
Eq(F_148(x), F_149(x)*F_4(x))
Eq(F_149(x), F_150(x) + F_163(x))
Eq(F_150(x), F_151(x) + F_159(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_153(x)*F_4(x))
Eq(F_153(x), F_154(x) + F_58(x))
Eq(F_154(x), F_151(x) + F_155(x))
Eq(F_155(x), F_156(x) + 2*F_20(x) + F_67(x))
Eq(F_156(x), F_157(x)*F_4(x))
Eq(F_157(x), F_158(x) + F_65(x))
Eq(F_158(x), F_155(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_161(x)*F_4(x))
Eq(F_161(x), F_144(x) + F_162(x))
Eq(F_162(x), F_159(x))
Eq(F_163(x), F_164(x) + F_165(x))
Eq(F_164(x), F_131(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_167(x)*F_4(x))
Eq(F_167(x), F_168(x) + F_170(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_97(x))
Eq(F_170(x), F_166(x))
Eq(F_171(x), F_172(x)*F_4(x))
Eq(F_172(x), F_173(x) + F_174(x))
Eq(F_173(x), F_136(x) + F_48(x))
Eq(F_174(x), F_175(x) + F_176(x))
Eq(F_175(x), F_152(x))
Eq(F_176(x), F_177(x))
Eq(F_177(x), F_178(x)*F_4(x))
Eq(F_178(x), F_179(x) + F_184(x))
Eq(F_179(x), F_169(x) + F_180(x))
Eq(F_180(x), F_181(x) + F_20(x) + F_87(x))
Eq(F_181(x), F_182(x)*F_4(x))
Eq(F_182(x), F_183(x) + F_52(x))
Eq(F_183(x), F_60(x))
Eq(F_184(x), F_185(x) + F_186(x))
Eq(F_185(x), F_177(x))
Eq(F_186(x), F_127(x) + F_187(x) + 3*F_20(x))
Eq(F_187(x), F_188(x)*F_4(x))
Eq(F_188(x), F_168(x) + F_189(x))
Eq(F_189(x), F_186(x))
Pack JSON:
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Specification JSON:
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