0123_0132_0213_0321_1203
Counting sequence:
1, 1, 2, 6, 19, 60, 188, 586, 1823, 5669, 17629, 54823, 170492, 530209, 1648886, 5127837, 15946955, 49593106, 154228574, 479632249, 1491598400, 4638690980, 14425769034, 44862400433, 139516650231, 433879941863, 1349314247721, 4196204441452, 13049689310107, 40582958591834, 126208102655051, 392491965309621, 1220602636374738, 3795926866298174, 11804874366878347, 36711734373766244, 114169062612935388, 355052003950832370, 1104168875739013311, 3433831924856816173, 10678802805661488885, 33209787740836730455, 103278431286952868764, 321183455080556357017, 998841776855258866534, 3106277360834605752141, 9660147649022317801659, 30041893160447937875882, 93426661522622811364630, 290545640271246585201729, 903561870935391560594648, 2809968354183772558500356, 8738662404313484808287042, 27176185277269388754910161, 84514655911174781143687535, 262830378543178594474140239, 817370752331449954336047705, 2541924379023499290878640172, 7905077995809990447289323779, 24583838384620014134022553034, 76452769984237248836095338267, 237758886420251458140889751845, 739401438083316459433177138810, 2299449222996988532951996267814, 7151009528528476438509250658083, 22238776471200222811363442175692, 69159910494173131431475069565948, 215078973690673376428648188627418, 668869647072935208055705663260255, 2080103866493729919121344654247221, 6468871945882089731055615010695053, 20117410926579070347472672321574343, 62562719709805143954467966817242620, 194562506665127095661508063654463185, 605065911063403900634542576561988886, 1881681948933312717241139976525698301, 5851803732784481567344029289925221483, 18198403267057112113468762865278601410, 56594837522489444454671003063695803534, 176003113415726422119420531986147464521, 547348438269117669465246871846824994800, 1702187575329975928575582372107969122020, 5293597896744416666064883652066503553018, 16462450495201564035753973604440019031793, 51196233940178158775768064487269989666023, 159214107913121970617380184700515628879415, 495136657672734963693614942923821799802185, 1539815239897605336888537652195076797250860, 4788639532700635074025477819961464708605611, 14892090934018958849032642631109245398373626, 46312605255133125470834377468197045959778027, 144026612180976480397059110476675243894096085, 447905379152261104314531359891256645030718882, 1392931664749865158065746677872834344104393038, 4331849343571421089332848791968753772426839931, 13471528582681656865610894618544165141993882036, 41894827811436484317139117601450537546024432796, 130287857578855731793771550725067738343125299714, 405179510675882664226099219157989612309456678911, 1260059371013793899168047855292227137005360728893, 3918632548400934928527144130227596335850018210981
Generating function in Maple syntax:
-(x-1)*(2*x^3-2*x^2+3*x-1)/(2*x^5-5*x^4+8*x^3-8*x^2+5*x-1)
Generating function in latex syntax:
-\frac{\left(x -1\right) \left(2 x^{3}-2 x^{2}+3 x -1\right)}{2 x^{5}-5 x^{4}+8 x^{3}-8 x^{2}+5 x -1}
Generating function in sympy syntax:
(1 - x)*(2*x**3 - 2*x**2 + 3*x - 1)/(2*x**5 - 5*x**4 + 8*x**3 - 8*x**2 + 5*x - 1)
Implicit equation for the generating function in Maple syntax:
(2*x^5-5*x^4+8*x^3-8*x^2+5*x-1)*F(x)+(x-1)*(2*x^3-2*x^2+3*x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{5}-5 x^{4}+8 x^{3}-8 x^{2}+5 x -1\right) F \! \left(x \right)+\left(x -1\right) \left(2 x^{3}-2 x^{2}+3 x -1\right) = 0
Explicit closed form in Maple syntax:
-3408/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+3)-3408/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n+3)-3408/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n+3)-3408/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 4)^(-n+3)-3408/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 5)^(-n+3)+7234/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+2)+7234/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n+2)+7234/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n+2)+7234/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 4)^(-n+2)+7234/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 5)^(-n+2)-9105/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+1)-9105/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n+1)-9105/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n+1)-9105/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 4)^(-n+1)-9105/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 5)^(-n+1)-1463/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n-1)-1463/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n-1)-1463/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n-1)-1463/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 4)^(-n-1)-1463/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 5)^(-n-1)+8984/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n)+8984/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n)+8984/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n)+8984/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 4)^(-n)+8984/10277*RootOf(2*_Z^5-5*_Z^4+8*_Z^3-8*_Z^2+5*_Z-1,index = 5)^(-n)
Explicit closed form in latex syntax:
-\frac{3408 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{10277}-\frac{3408 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{10277}-\frac{3408 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{10277}-\frac{3408 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{10277}-\frac{3408 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{10277}+\frac{7234 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{10277}+\frac{7234 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{10277}+\frac{7234 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{10277}+\frac{7234 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{10277}+\frac{7234 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{10277}-\frac{9105 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{10277}-\frac{9105 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{10277}-\frac{9105 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{10277}-\frac{9105 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{10277}-\frac{9105 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{10277}-\frac{1463 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{10277}-\frac{1463 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{10277}-\frac{1463 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{10277}-\frac{1463 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{10277}-\frac{1463 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{10277}+\frac{8984 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{10277}+\frac{8984 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{10277}+\frac{8984 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{10277}+\frac{8984 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{10277}+\frac{8984 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{10277}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n+5) = 2*a(n)-5*a(n+1)+8*a(n+2)-8*a(n+3)+5*a(n+4), 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) = 19
a \! \left(n +5\right) = 2 a \! \left(n \right)-5 a \! \left(n +1\right)+8 a \! \left(n +2\right)-8 a \! \left(n +3\right)+5 a \! \left(n +4\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15960/
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[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[14,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[4,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[4,x]
F[16,x] = F[17,x]+F[2,x]
F[17,x] = F[137,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[34,x]
F[21,x] = F[22,x]+F[7,x]
F[22,x] = F[18,x]+F[23,x]+F[27,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[4,x]
F[26,x] = F[14,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[11,x]+F[29,x]
F[29,x] = F[30,x]+F[32,x]
F[30,x] = F[31,x]
F[31,x] = F[25,x]*F[4,x]
F[32,x] = F[33,x]
F[33,x] = F[30,x]*F[4,x]
F[34,x] = F[17,x]+F[35,x]
F[35,x] = F[122,x]+F[135,x]+F[18,x]+F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[46,x]
F[38,x] = F[22,x]+F[39,x]
F[39,x] = F[18,x]+F[40,x]+F[41,x]+F[44,x]
F[40,x] = 0
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[26,x]+F[43,x]
F[43,x] = F[32,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[29,x]
F[46,x] = F[35,x]+F[47,x]
F[47,x] = F[118,x]+F[133,x]+F[18,x]+F[48,x]+F[87,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[54,x]
F[50,x] = F[39,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[43,x]
F[54,x] = F[47,x]+F[55,x]
F[55,x] = F[132,x]+F[18,x]+F[56,x]+F[60,x]+F[61,x]+F[62,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[51,x]
F[59,x] = F[55,x]
F[60,x] = 0
F[61,x] = 0
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = 2*F[18,x]+F[131,x]+F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[73,x]
F[70,x] = F[30,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[26,x]*F[4,x]
F[73,x] = F[67,x]+F[74,x]
F[74,x] = 2*F[18,x]+F[75,x]+F[87,x]+F[88,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]+F[80,x]
F[77,x] = F[71,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[4,x]*F[43,x]
F[80,x] = F[74,x]+F[81,x]
F[81,x] = 2*F[18,x]+F[60,x]+F[61,x]+F[82,x]+F[86,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[78,x]
F[85,x] = F[81,x]
F[86,x] = F[4,x]*F[64,x]
F[87,x] = 0
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[91,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[129,x]+F[18,x]+F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[95,x]+F[98,x]
F[95,x] = F[12,x]+F[96,x]
F[96,x] = F[18,x]+F[23,x]+F[97,x]
F[97,x] = F[11,x]*F[4,x]
F[98,x] = F[92,x]+F[99,x]
F[99,x] = F[100,x]+F[122,x]+F[127,x]+F[18,x]
F[100,x] = F[101,x]*F[4,x]
F[101,x] = F[102,x]+F[105,x]
F[102,x] = F[103,x]+F[96,x]
F[103,x] = F[104,x]+F[18,x]+F[40,x]+F[41,x]
F[104,x] = F[29,x]*F[4,x]
F[105,x] = F[106,x]+F[99,x]
F[106,x] = F[107,x]+F[118,x]+F[120,x]+F[18,x]+F[87,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[109,x]+F[111,x]
F[109,x] = F[103,x]+F[110,x]
F[110,x] = F[52,x]
F[111,x] = F[106,x]+F[112,x]
F[112,x] = F[113,x]+F[117,x]+F[18,x]+F[60,x]+F[61,x]+F[62,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[115,x]+F[116,x]
F[115,x] = F[110,x]
F[116,x] = F[112,x]
F[117,x] = 0
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[64,x]+F[89,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[65,x]+F[67,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[124,x]+F[89,x]
F[124,x] = F[125,x]
F[125,x] = F[126,x]
F[126,x] = F[2,x]*F[4,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[90,x]+F[92,x]
F[129,x] = F[130,x]*F[4,x]
F[130,x] = F[125,x]+F[2,x]
F[131,x] = F[124,x]*F[4,x]
F[132,x] = 0
F[133,x] = F[134,x]*F[4,x]
F[134,x] = F[121,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[121,x]+F[128,x]
F[137,x] = F[138,x]*F[4,x]
F[138,x] = F[128,x]+F[130,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_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \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_{137}\! \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_{34}\! \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_{27}\! \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_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \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_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{32}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{17}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{122}\! \left(x \right)+F_{135}\! \left(x \right)+F_{18}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{46}\! \left(x \right)
F_{38}\! \left(x \right) = F_{22}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{18}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{40}\! \left(x \right) = 0
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{26}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{32}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{29}\! \left(x \right)
F_{46}\! \left(x \right) = F_{35}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{118}\! \left(x \right)+F_{133}\! \left(x \right)+F_{18}\! \left(x \right)+F_{48}\! \left(x \right)+F_{87}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{50}\! \left(x \right) = F_{39}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{43}\! \left(x \right)
F_{54}\! \left(x \right) = F_{47}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{132}\! \left(x \right)+F_{18}\! \left(x \right)+F_{56}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{62}\! \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_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{51}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = 0
F_{61}\! \left(x \right) = 0
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_{64}\! \left(x \right) = F_{65}\! \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) = 2 F_{18}\! \left(x \right)+F_{131}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{73}\! \left(x \right)
F_{70}\! \left(x \right) = F_{30}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{73}\! \left(x \right) = F_{67}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{75}\! \left(x \right)+F_{87}\! \left(x \right)+F_{88}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{80}\! \left(x \right)
F_{77}\! \left(x \right) = F_{71}\! \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_{43}\! \left(x \right)
F_{80}\! \left(x \right) = F_{74}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{78}\! \left(x \right)
F_{85}\! \left(x \right) = F_{81}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{87}\! \left(x \right) = 0
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_{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_{129}\! \left(x \right)+F_{18}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{98}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{98}\! \left(x \right) = F_{92}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{122}\! \left(x \right)+F_{127}\! \left(x \right)+F_{18}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{105}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{96}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{18}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{104}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{99}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{118}\! \left(x \right)+F_{120}\! \left(x \right)+F_{18}\! \left(x \right)+F_{87}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{111}\! \left(x \right)
F_{109}\! \left(x \right) = F_{103}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{52}\! \left(x \right)
F_{111}\! \left(x \right) = F_{106}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{117}\! \left(x \right)+F_{18}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{62}\! \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_{110}\! \left(x \right)
F_{116}\! \left(x \right) = F_{112}\! \left(x \right)
F_{117}\! \left(x \right) = 0
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{64}\! \left(x \right)+F_{89}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{4}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{89}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{125}\! \left(x \right)+F_{2}\! \left(x \right)
F_{131}\! \left(x \right) = F_{124}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = 0
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = F_{121}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{121}\! \left(x \right)+F_{128}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{4}\! \left(x \right)
F_{138}\! \left(x \right) = F_{128}\! \left(x \right)+F_{130}\! \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_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_14(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_4(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_2(x))
Eq(F_17(x), F_137(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_34(x))
Eq(F_21(x), F_22(x) + F_7(x))
Eq(F_22(x), F_18(x) + F_23(x) + F_27(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_4(x))
Eq(F_26(x), F_14(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_11(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_32(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_25(x)*F_4(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_30(x)*F_4(x))
Eq(F_34(x), F_17(x) + F_35(x))
Eq(F_35(x), F_122(x) + F_135(x) + F_18(x) + F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_46(x))
Eq(F_38(x), F_22(x) + F_39(x))
Eq(F_39(x), F_18(x) + F_40(x) + F_41(x) + F_44(x))
Eq(F_40(x), 0)
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_26(x) + F_43(x))
Eq(F_43(x), F_32(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_29(x))
Eq(F_46(x), F_35(x) + F_47(x))
Eq(F_47(x), F_118(x) + F_133(x) + F_18(x) + F_48(x) + F_87(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_54(x))
Eq(F_50(x), F_39(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_43(x))
Eq(F_54(x), F_47(x) + F_55(x))
Eq(F_55(x), F_132(x) + F_18(x) + F_56(x) + F_60(x) + F_61(x) + F_62(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_51(x))
Eq(F_59(x), F_55(x))
Eq(F_60(x), 0)
Eq(F_61(x), 0)
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_131(x) + 2*F_18(x) + F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_73(x))
Eq(F_70(x), F_30(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_26(x)*F_4(x))
Eq(F_73(x), F_67(x) + F_74(x))
Eq(F_74(x), 2*F_18(x) + F_75(x) + F_87(x) + F_88(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_80(x))
Eq(F_77(x), F_71(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(x)*F_43(x))
Eq(F_80(x), F_74(x) + F_81(x))
Eq(F_81(x), 2*F_18(x) + F_60(x) + F_61(x) + F_82(x) + F_86(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_78(x))
Eq(F_85(x), F_81(x))
Eq(F_86(x), F_4(x)*F_64(x))
Eq(F_87(x), 0)
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_129(x) + F_18(x) + F_93(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_98(x))
Eq(F_95(x), F_12(x) + F_96(x))
Eq(F_96(x), F_18(x) + F_23(x) + F_97(x))
Eq(F_97(x), F_11(x)*F_4(x))
Eq(F_98(x), F_92(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_122(x) + F_127(x) + F_18(x))
Eq(F_100(x), F_101(x)*F_4(x))
Eq(F_101(x), F_102(x) + F_105(x))
Eq(F_102(x), F_103(x) + F_96(x))
Eq(F_103(x), F_104(x) + F_18(x) + F_40(x) + F_41(x))
Eq(F_104(x), F_29(x)*F_4(x))
Eq(F_105(x), F_106(x) + F_99(x))
Eq(F_106(x), F_107(x) + F_118(x) + F_120(x) + F_18(x) + F_87(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_109(x) + F_111(x))
Eq(F_109(x), F_103(x) + F_110(x))
Eq(F_110(x), F_52(x))
Eq(F_111(x), F_106(x) + F_112(x))
Eq(F_112(x), F_113(x) + F_117(x) + F_18(x) + F_60(x) + F_61(x) + F_62(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_110(x))
Eq(F_116(x), F_112(x))
Eq(F_117(x), 0)
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_64(x) + F_89(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_65(x) + F_67(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_124(x) + F_89(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_2(x)*F_4(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_90(x) + F_92(x))
Eq(F_129(x), F_130(x)*F_4(x))
Eq(F_130(x), F_125(x) + F_2(x))
Eq(F_131(x), F_124(x)*F_4(x))
Eq(F_132(x), 0)
Eq(F_133(x), F_134(x)*F_4(x))
Eq(F_134(x), F_121(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_121(x) + F_128(x))
Eq(F_137(x), F_138(x)*F_4(x))
Eq(F_138(x), F_128(x) + F_130(x))
Pack JSON:
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Specification JSON:
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