0123_0213_1302_2130
Counting sequence:
1, 1, 2, 6, 20, 63, 186, 523, 1426, 3820, 10136, 26761, 70468, 185283, 486712, 1277670, 3352276, 8791787, 23049574, 60412075, 158300630, 414723992, 1086350032, 2845300501, 7451528160, 19513282883, 51096392396, 133792158498, 350312806796, 917212025895, 2401455311826, 6287418822091, 16461332324218, 43097642666788, 112833728231432, 295407812839105, 773398261134556, 2024804087190147, 5301048257842624, 13878409240236990, 36334316633910340, 95124815105909507, 249040677738226462, 651998316485497771, 1706956468905213950, 4468875485305443728, 11699678778296616256, 30630178433991711373, 80190891695464341816, 209942567000780484995, 549636950011414192916, 1438968564455122517946, 3767269306217639215868, 9862840479958118114943, 25821254385230677385802, 67600927178968106122315, 176981536158281608997986, 463343699309318508333532, 1213049597796922926216824, 3175805166136539577469305, 8314366044723831142515700, 21767293256258772531476547, 56987514300502628545486792, 149195250798153450031660566, 390598240399772952873161140, 1022599475012806481445005723, 2677200193861945804856391766, 7009001125019657337803268523, 18349803218090323963481816486, 48040408603037982785959226120, 125771422738597078530060404656, 329273859907900351468041773701, 862050157575398481263225649168, 2256876613998884601553968509123, 5908579686782435148378879588572, 15468862451070781798512614596050, 40498007675874634268503930846316, 106025160595442572466143734132567, 277577474148231991576156084804674, 726707261924811228099176470568395, 1902544311777317358867411252139210, 4980925673709372204211861484782612, 13040232709955262003074843973207272, 34139772457365339364931802698435761, 89379084664558607310753681744035980, 233997481541146185165896121593898243, 612613359968551353643763938069220176, 1603842598383850687099250343404361198, 4198914435221686331001588031363659556, 10992900707358579553700803407492297395, 28779787687008794827471380920729292046, 75346462353977289926334524008298498731, 197259599375542044951434607021747559118, 516432335773886784935314242696853219328, 1352037407948594189881398172763752040992, 3539679888076847544782400653204150994685, 9267002256291851964644784976703187208296, 24261326880818515389561597365469241466627, 63516978386203308284942914440322047269924, 166289608277870637627208262449076627228010, 435351846447567060920783028889901843334620
Generating function in Maple syntax:
-(2*x^9+2*x^8+3*x^7-8*x^6+3*x^5+20*x^4-36*x^3+25*x^2-8*x+1)/(2*x-1)/(x^2-3*x+1)/(x^2+x-1)/(x-1)^3
Generating function in latex syntax:
-\frac{2 x^{9}+2 x^{8}+3 x^{7}-8 x^{6}+3 x^{5}+20 x^{4}-36 x^{3}+25 x^{2}-8 x +1}{\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-2*x**9 - 2*x**8 - 3*x**7 + 8*x**6 - 3*x**5 - 20*x**4 + 36*x**3 - 25*x**2 + 8*x - 1)/((x - 1)**3*(2*x - 1)*(x**2 - 3*x + 1)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^2-3*x+1)*(x^2+x-1)*(x-1)^3*F(x)+2*x^9+2*x^8+3*x^7-8*x^6+3*x^5+20*x^4-36*x^3+25*x^2-8*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+2 x^{9}+2 x^{8}+3 x^{7}-8 x^{6}+3 x^{5}+20 x^{4}-36 x^{3}+25 x^{2}-8 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/20*(-81*5^(1/2)+195)*(3/2-1/2*5^(1/2))^(-n)+1/20*(81*5^(1/2)+195)*(3/2+1/2*5^(1/2))^(-n)+1/20*(-11*5^(1/2)+25)*(-1/2*5^(1/2)-1/2)^(-n)+1/20*(11*5^(1/2)+25)*(1/2*5^(1/2)-1/2)^(-n)-2*n^2+6*n-2^(-1+n)-14)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(-81 \sqrt{5}+195\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{20}+\frac{\left(81 \sqrt{5}+195\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{20}+\\\frac{\left(-11 \sqrt{5}+25\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{20}+\frac{\left(11 \sqrt{5}+25\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{20}-2 n^{2}+6 n \\-2^{-1+n}-14 & \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) = 63
a(6) = 186
a(7) = 523
a(8) = 1426
a(9) = 3820
a(n+5) = 2*n^2-2*a(n)+5*a(n+1)+4*a(n+2)-11*a(n+3)+6*a(n+4)-10*n+6, n >= 10
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) = 63
a \! \left(6\right) = 186
a \! \left(7\right) = 523
a \! \left(8\right) = 1426
a \! \left(9\right) = 3820
a \! \left(n +5\right) = 2 n^{2}-2 a \! \left(n \right)+5 a \! \left(n +1\right)+4 a \! \left(n +2\right)-11 a \! \left(n +3\right)+6 a \! \left(n +4\right)-10 n +6, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14933/
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[16,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[7,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[4,x]
F[16,x] = F[17,x]+F[2,x]
F[17,x] = F[141,x]+F[18,x]+F[19,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[35,x]
F[21,x] = F[22,x]+F[7,x]
F[22,x] = F[18,x]+F[23,x]+F[29,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]
F[25,x] = F[11,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[11,x]+F[26,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[13,x]+F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[29,x]
F[33,x] = F[34,x]
F[34,x] = F[31,x]*F[4,x]
F[35,x] = F[36,x]+F[70,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[43,x]
F[39,x] = F[40,x]+F[7,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[11,x]
F[43,x] = F[36,x]+F[44,x]
F[44,x] = 2*F[18,x]+F[45,x]+F[53,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[40,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[40,x]
F[52,x] = F[49,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[60,x]
F[58,x] = F[11,x]+F[59,x]
F[59,x] = F[41,x]
F[60,x] = F[55,x]+F[61,x]
F[61,x] = 2*F[18,x]+F[53,x]+F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[59,x]
F[65,x] = F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[59,x]
F[69,x] = F[66,x]
F[70,x] = 2*F[18,x]+F[123,x]+F[71,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]+F[77,x]
F[73,x] = F[22,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[26,x]
F[77,x] = F[112,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[81,x]+F[85,x]
F[81,x] = F[22,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[26,x]
F[85,x] = F[78,x]+F[86,x]
F[86,x] = 3*F[18,x]+F[87,x]+F[95,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[82,x]
F[90,x] = F[91,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[82,x]
F[94,x] = F[91,x]
F[95,x] = F[4,x]*F[96,x]
F[96,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[102,x]
F[100,x] = F[101,x]+F[26,x]
F[101,x] = F[83,x]
F[102,x] = F[103,x]+F[97,x]
F[103,x] = 3*F[18,x]+F[104,x]+F[95,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[101,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[101,x]
F[111,x] = F[108,x]
F[112,x] = 3*F[18,x]+F[113,x]+F[121,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[115,x]+F[116,x]
F[115,x] = F[74,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[4,x]
F[118,x] = F[119,x]+F[120,x]
F[119,x] = F[74,x]
F[120,x] = F[117,x]
F[121,x] = F[122,x]*F[4,x]
F[122,x] = F[97,x]
F[123,x] = F[124,x]*F[4,x]
F[124,x] = F[125,x]
F[125,x] = F[126,x]+F[55,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[129,x]+F[131,x]
F[129,x] = F[130,x]+F[26,x]
F[130,x] = F[75,x]
F[131,x] = F[132,x]+F[97,x]
F[132,x] = 3*F[18,x]+F[121,x]+F[133,x]
F[133,x] = F[134,x]*F[4,x]
F[134,x] = F[135,x]+F[136,x]
F[135,x] = F[130,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[130,x]
F[140,x] = F[137,x]
F[141,x] = F[142,x]*F[4,x]
F[142,x] = F[143,x]+F[183,x]
F[143,x] = F[144,x]+F[2,x]
F[144,x] = F[145,x]+F[18,x]+F[180,x]
F[145,x] = F[146,x]*F[4,x]
F[146,x] = F[147,x]+F[149,x]
F[147,x] = F[11,x]+F[148,x]
F[148,x] = F[15,x]+F[18,x]+F[23,x]
F[149,x] = F[150,x]+F[55,x]
F[150,x] = 2*F[18,x]+F[123,x]+F[151,x]
F[151,x] = F[152,x]*F[4,x]
F[152,x] = F[153,x]+F[155,x]
F[153,x] = F[148,x]+F[154,x]
F[154,x] = F[75,x]
F[155,x] = F[156,x]+F[171,x]
F[156,x] = F[157,x]
F[157,x] = F[158,x]*F[4,x]
F[158,x] = F[159,x]+F[161,x]
F[159,x] = F[148,x]+F[160,x]
F[160,x] = F[83,x]
F[161,x] = F[156,x]+F[162,x]
F[162,x] = 3*F[18,x]+F[163,x]+F[95,x]
F[163,x] = F[164,x]*F[4,x]
F[164,x] = F[165,x]+F[166,x]
F[165,x] = F[160,x]
F[166,x] = F[167,x]
F[167,x] = F[168,x]*F[4,x]
F[168,x] = F[169,x]+F[170,x]
F[169,x] = F[160,x]
F[170,x] = F[167,x]
F[171,x] = 3*F[18,x]+F[121,x]+F[172,x]
F[172,x] = F[173,x]*F[4,x]
F[173,x] = F[174,x]+F[175,x]
F[174,x] = F[154,x]
F[175,x] = F[176,x]
F[176,x] = F[177,x]*F[4,x]
F[177,x] = F[178,x]+F[179,x]
F[178,x] = F[154,x]
F[179,x] = F[176,x]
F[180,x] = F[181,x]*F[4,x]
F[181,x] = F[182,x]+F[2,x]
F[182,x] = F[180,x]
F[183,x] = F[184,x]+F[190,x]
F[184,x] = F[185,x]
F[185,x] = F[186,x]*F[4,x]
F[186,x] = F[181,x]+F[187,x]
F[187,x] = F[184,x]+F[188,x]
F[188,x] = F[189,x]
F[189,x] = F[187,x]*F[4,x]
F[190,x] = F[189,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_{16}\! \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_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{141}\! \left(x \right)+F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{35}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{7}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)+F_{29}\! \left(x \right)
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_{25}\! \left(x \right) = F_{11}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right)+F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{13}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{29}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{70}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{43}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{7}\! \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_{11}\! \left(x \right)
F_{43}\! \left(x \right) = F_{36}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{45}\! \left(x \right)+F_{53}\! \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_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{40}\! \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_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{40}\! \left(x \right)
F_{52}\! \left(x \right) = F_{49}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \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_{60}\! \left(x \right)
F_{58}\! \left(x \right) = F_{11}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{41}\! \left(x \right)
F_{60}\! \left(x \right) = F_{55}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{53}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{59}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{59}\! \left(x \right)
F_{69}\! \left(x \right) = F_{66}\! \left(x \right)
F_{70}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{123}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{77}\! \left(x \right)
F_{73}\! \left(x \right) = F_{22}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{26}\! \left(x \right)
F_{77}\! \left(x \right) = F_{112}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{85}\! \left(x \right)
F_{81}\! \left(x \right) = F_{22}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \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_{26}\! \left(x \right)
F_{85}\! \left(x \right) = F_{78}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{87}\! \left(x \right)+F_{95}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{82}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \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_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{82}\! \left(x \right)
F_{94}\! \left(x \right) = F_{91}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \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_{102}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{26}\! \left(x \right)
F_{101}\! \left(x \right) = F_{83}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{97}\! \left(x \right)
F_{103}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{104}\! \left(x \right)+F_{95}\! \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_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{101}\! \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_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{101}\! \left(x \right)
F_{111}\! \left(x \right) = F_{108}\! \left(x \right)
F_{112}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{113}\! \left(x \right)+F_{121}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{116}\! \left(x \right)
F_{115}\! \left(x \right) = F_{74}\! \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_{120}\! \left(x \right)
F_{119}\! \left(x \right) = F_{74}\! \left(x \right)
F_{120}\! \left(x \right) = F_{117}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{4}\! \left(x \right)
F_{122}\! \left(x \right) = F_{97}\! \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_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{55}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{131}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{26}\! \left(x \right)
F_{130}\! \left(x \right) = F_{75}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{97}\! \left(x \right)
F_{132}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{121}\! \left(x \right)+F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{136}\! \left(x \right)
F_{135}\! \left(x \right) = F_{130}\! \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_{130}\! \left(x \right)
F_{140}\! \left(x \right) = F_{137}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{4}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{183}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{2}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{18}\! \left(x \right)+F_{180}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{4}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{149}\! \left(x \right)
F_{147}\! \left(x \right) = F_{11}\! \left(x \right)+F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)+F_{23}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{55}\! \left(x \right)
F_{150}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{123}\! \left(x \right)+F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{4}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{155}\! \left(x \right)
F_{153}\! \left(x \right) = F_{148}\! \left(x \right)+F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{75}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{171}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{4}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{161}\! \left(x \right)
F_{159}\! \left(x \right) = F_{148}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{83}\! \left(x \right)
F_{161}\! \left(x \right) = F_{156}\! \left(x \right)+F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{163}\! \left(x \right)+F_{95}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right) F_{4}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{166}\! \left(x \right)
F_{165}\! \left(x \right) = F_{160}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right) F_{4}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{170}\! \left(x \right)
F_{169}\! \left(x \right) = F_{160}\! \left(x \right)
F_{170}\! \left(x \right) = F_{167}\! \left(x \right)
F_{171}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{121}\! \left(x \right)+F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right) F_{4}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)+F_{175}\! \left(x \right)
F_{174}\! \left(x \right) = F_{154}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right) F_{4}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{179}\! \left(x \right)
F_{178}\! \left(x \right) = F_{154}\! \left(x \right)
F_{179}\! \left(x \right) = F_{176}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right) F_{4}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{2}\! \left(x \right)
F_{182}\! \left(x \right) = F_{180}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{190}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right) F_{4}\! \left(x \right)
F_{186}\! \left(x \right) = F_{181}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{184}\! \left(x \right)+F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{187}\! \left(x \right) F_{4}\! \left(x \right)
F_{190}\! \left(x \right) = F_{189}\! \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_16(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_7(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_2(x))
Eq(F_17(x), F_141(x) + F_18(x) + F_19(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_35(x))
Eq(F_21(x), F_22(x) + F_7(x))
Eq(F_22(x), F_18(x) + F_23(x) + F_29(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_11(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_11(x) + F_26(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_13(x) + F_31(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_29(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_31(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_70(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_43(x))
Eq(F_39(x), F_40(x) + F_7(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_11(x))
Eq(F_43(x), F_36(x) + F_44(x))
Eq(F_44(x), 2*F_18(x) + F_45(x) + F_53(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_40(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_52(x))
Eq(F_51(x), F_40(x))
Eq(F_52(x), F_49(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_60(x))
Eq(F_58(x), F_11(x) + F_59(x))
Eq(F_59(x), F_41(x))
Eq(F_60(x), F_55(x) + F_61(x))
Eq(F_61(x), 2*F_18(x) + F_53(x) + F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_59(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_59(x))
Eq(F_69(x), F_66(x))
Eq(F_70(x), F_123(x) + 2*F_18(x) + F_71(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_77(x))
Eq(F_73(x), F_22(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_26(x))
Eq(F_77(x), F_112(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_85(x))
Eq(F_81(x), F_22(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_26(x))
Eq(F_85(x), F_78(x) + F_86(x))
Eq(F_86(x), 3*F_18(x) + F_87(x) + F_95(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_82(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_82(x))
Eq(F_94(x), F_91(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(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_102(x))
Eq(F_100(x), F_101(x) + F_26(x))
Eq(F_101(x), F_83(x))
Eq(F_102(x), F_103(x) + F_97(x))
Eq(F_103(x), F_104(x) + 3*F_18(x) + F_95(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_101(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_101(x))
Eq(F_111(x), F_108(x))
Eq(F_112(x), F_113(x) + F_121(x) + 3*F_18(x))
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_115(x) + F_116(x))
Eq(F_115(x), F_74(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_120(x))
Eq(F_119(x), F_74(x))
Eq(F_120(x), F_117(x))
Eq(F_121(x), F_122(x)*F_4(x))
Eq(F_122(x), F_97(x))
Eq(F_123(x), F_124(x)*F_4(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_126(x) + F_55(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_129(x) + F_131(x))
Eq(F_129(x), F_130(x) + F_26(x))
Eq(F_130(x), F_75(x))
Eq(F_131(x), F_132(x) + F_97(x))
Eq(F_132(x), F_121(x) + F_133(x) + 3*F_18(x))
Eq(F_133(x), F_134(x)*F_4(x))
Eq(F_134(x), F_135(x) + F_136(x))
Eq(F_135(x), F_130(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_130(x))
Eq(F_140(x), F_137(x))
Eq(F_141(x), F_142(x)*F_4(x))
Eq(F_142(x), F_143(x) + F_183(x))
Eq(F_143(x), F_144(x) + F_2(x))
Eq(F_144(x), F_145(x) + F_18(x) + F_180(x))
Eq(F_145(x), F_146(x)*F_4(x))
Eq(F_146(x), F_147(x) + F_149(x))
Eq(F_147(x), F_11(x) + F_148(x))
Eq(F_148(x), F_15(x) + F_18(x) + F_23(x))
Eq(F_149(x), F_150(x) + F_55(x))
Eq(F_150(x), F_123(x) + F_151(x) + 2*F_18(x))
Eq(F_151(x), F_152(x)*F_4(x))
Eq(F_152(x), F_153(x) + F_155(x))
Eq(F_153(x), F_148(x) + F_154(x))
Eq(F_154(x), F_75(x))
Eq(F_155(x), F_156(x) + F_171(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_158(x)*F_4(x))
Eq(F_158(x), F_159(x) + F_161(x))
Eq(F_159(x), F_148(x) + F_160(x))
Eq(F_160(x), F_83(x))
Eq(F_161(x), F_156(x) + F_162(x))
Eq(F_162(x), F_163(x) + 3*F_18(x) + F_95(x))
Eq(F_163(x), F_164(x)*F_4(x))
Eq(F_164(x), F_165(x) + F_166(x))
Eq(F_165(x), F_160(x))
Eq(F_166(x), F_167(x))
Eq(F_167(x), F_168(x)*F_4(x))
Eq(F_168(x), F_169(x) + F_170(x))
Eq(F_169(x), F_160(x))
Eq(F_170(x), F_167(x))
Eq(F_171(x), F_121(x) + F_172(x) + 3*F_18(x))
Eq(F_172(x), F_173(x)*F_4(x))
Eq(F_173(x), F_174(x) + F_175(x))
Eq(F_174(x), F_154(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_177(x)*F_4(x))
Eq(F_177(x), F_178(x) + F_179(x))
Eq(F_178(x), F_154(x))
Eq(F_179(x), F_176(x))
Eq(F_180(x), F_181(x)*F_4(x))
Eq(F_181(x), F_182(x) + F_2(x))
Eq(F_182(x), F_180(x))
Eq(F_183(x), F_184(x) + F_190(x))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_186(x)*F_4(x))
Eq(F_186(x), F_181(x) + F_187(x))
Eq(F_187(x), F_184(x) + F_188(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_187(x)*F_4(x))
Eq(F_190(x), F_189(x))
Pack JSON:
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Specification JSON:
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