0123_0213_0231_2130_3021
Counting sequence:
1, 1, 2, 6, 19, 52, 117, 241, 476, 920, 1757, 3330, 6278, 11790, 22074, 41226, 76836, 142955, 265574, 492736, 913191, 1690799, 3127954, 5782477, 10683001, 19725749, 36405331, 67160521, 123852167, 228325050, 420805363, 775357267, 1428330026, 2630709726, 4844456475, 8919772796, 16421275068, 30228117028, 55638113704, 102399067356, 188445808514, 346775061617, 638092520020, 1174078044794, 2160182863677, 3974355320453, 7311855358208, 13451634563663, 24746325393015, 45523536486987, 83743697766545, 154049482141619, 283374840213197, 521262066434576, 958838558920753, 1763721682013205, 3244220693944680, 5967425537899572, 10976410903454649, 20189744727917142, 37136311751486914, 68306885557692618, 125640090794146262, 231094855035209422, 425060547075981648, 781825775526154439, 1438030175947096098, 2644995779479800020, 4864980010193369123, 8948213525791151787, 16458525154875526190, 30272262090442139057, 55679880010102114405, 102412089893995169137, 188366533872108109615, 346462228292349469821, 637246878452165512419, 1172085391526479932534, 2155810275574564519471, 3965168073766636409975, 7293105046384676912406, 13414150229456300338010, 24672531488855032207159, 45379961737673850500688, 83466926568210442635928, 153519877879942425977152, 282367507383255079337412, 519355511114039408807712, 955244836857296735203342, 1756970995117282505286957, 3231576423331369752317776, 5943800475311391377766542, 10932361194008237123349721, 20107759612904634126371169, 36983956102726091988403228, 68024133250394428471977267, 125115940127282449181520835, 230124176982415729470523879, 423264489023362661547413933, 778504992298343654451473383, 1431894283132674914144818121
Generating function in Maple syntax:
(2*x^11+7*x^10+9*x^9+2*x^8-9*x^7-13*x^6-x^5+3*x^4+3*x^3+2*x^2-3*x+1)/(x^2+x-1)/(x^3+x^2+x-1)/(x-1)^2
Generating function in latex syntax:
\frac{2 x^{11}+7 x^{10}+9 x^{9}+2 x^{8}-9 x^{7}-13 x^{6}-x^{5}+3 x^{4}+3 x^{3}+2 x^{2}-3 x +1}{\left(x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(2*x**11 + 7*x**10 + 9*x**9 + 2*x**8 - 9*x**7 - 13*x**6 - x**5 + 3*x**4 + 3*x**3 + 2*x**2 - 3*x + 1)/((x - 1)**2*(x**2 + x - 1)*(x**3 + x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
-(x^2+x-1)*(x^3+x^2+x-1)*(x-1)^2*F(x)+2*x^11+7*x^10+9*x^9+2*x^8-9*x^7-13*x^6-x^5+3*x^4+3*x^3+2*x^2-3*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+2 x^{11}+7 x^{10}+9 x^{9}+2 x^{8}-9 x^{7}-13 x^{6}-x^{5}+3 x^{4}+3 x^{3}+2 x^{2}-3 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,n = 2,2,n = 3,6,n = 4,19,1/2640*(((1705*I-395*11^(1/2))*3^(1/2)-1185*I*11^(1/2)+1705)*(17+3*11^(1/2)*3^(1/2))^(1/3)+4400+((2530*I+400*11^(1/2))*3^(1/2)-1200*I*11^(1/2)-2530)*(17+3*11^(1/2)*3^(1/2))^(2/3))*(1/24*((17*I+3*11^(1/2))*3^(1/2)-9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/2640*(((-2530*I+400*11^(1/2))*3^(1/2)+1200*I*11^(1/2)-2530)*(17+3*11^(1/2)*3^(1/2))^(2/3)+4400+((-1705*I-395*11^(1/2))*3^(1/2)+1185*I*11^(1/2)+1705)*(17+3*11^(1/2)*3^(1/2))^(1/3))*(1/24*((-17*I+3*11^(1/2))*3^(1/2)+9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)+1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/2640*((-800*11^(1/2)*3^(1/2)+5060)*(17+3*11^(1/2)*3^(1/2))^(2/3)+790*(17+3*11^(1/2)*3^(1/2))^(1/3)*11^(1/2)*3^(1/2)-3410*(17+3*11^(1/2)*3^(1/2))^(1/3)+4400)*(1/3*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3+17/12*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/4*(17+3*11^(1/2)*3^(1/2))^(2/3)*11^(1/2)*3^(1/2))^(-n)+1/2640*(1584*5^(1/2)-5280)*(-1/2*5^(1/2)-1/2)^(-n)+1/2640*(-1584*5^(1/2)-5280)*(1/2*5^(1/2)-1/2)^(-n)+3/2*n-22)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ 2 & n =2 \\ 6 & n =3 \\ 19 & n =4 \\ \frac{\left(\left(\left(1705 \,\mathrm{I}-395 \sqrt{11}\right) \sqrt{3}-1185 \,\mathrm{I} \sqrt{11}+1705\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+4400+\left(\left(2530 \,\mathrm{I}+400 \sqrt{11}\right) \sqrt{3}-1200 \,\mathrm{I} \sqrt{11}-2530\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}-9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}-\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{2640}\\+\\\frac{\left(\left(\left(-2530 \,\mathrm{I}+400 \sqrt{11}\right) \sqrt{3}+1200 \,\mathrm{I} \sqrt{11}-2530\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+4400+\left(\left(-1705 \,\mathrm{I}-395 \sqrt{11}\right) \sqrt{3}+1185 \,\mathrm{I} \sqrt{11}+1705\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{\left(\left(-17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}+9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}+\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{2640}\\+\\\frac{\left(\left(-800 \sqrt{11}\, \sqrt{3}+5060\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+790 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{11}\, \sqrt{3}-3410 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+4400\right) \left(\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{3}-\frac{1}{3}+\frac{17 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{12}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{11}\, \sqrt{3}}{4}\right)^{-n}}{2640}\\+\frac{\left(1584 \sqrt{5}-5280\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{2640}+\frac{\left(-1584 \sqrt{5}-5280\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{2640}\\+\frac{3 n}{2}-22 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 52
a(6) = 117
a(7) = 241
a(8) = 476
a(9) = 920
a(10) = 1757
a(11) = 3330
a(n+5) = -a(n)-2*a(n+1)-a(n+2)+a(n+3)+2*a(n+4)+3*n-47, n >= 12
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 52
a \! \left(6\right) = 117
a \! \left(7\right) = 241
a \! \left(8\right) = 476
a \! \left(9\right) = 920
a \! \left(10\right) = 1757
a \! \left(11\right) = 3330
a \! \left(n +5\right) = -a \! \left(n \right)-2 a \! \left(n +1\right)-a \! \left(n +2\right)+a \! \left(n +3\right)+2 a \! \left(n +4\right)+3 n -47, \quad n \geq 12
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16789/
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[18,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[14,x] = F[15,x]*F[4,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[1,x]+F[4,x]
F[17,x] = F[14,x]
F[18,x] = F[19,x]+F[58,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[16,x]*F[4,x]
F[25,x] = F[19,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]+F[54,x]
F[27,x] = 0
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[34,x]
F[30,x] = F[23,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[4,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[28,x]
F[36,x] = 2*F[27,x]+F[37,x]+F[41,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[31,x]
F[40,x] = F[37,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[48,x]
F[46,x] = F[4,x]+F[47,x]
F[47,x] = F[32,x]
F[48,x] = F[43,x]+F[49,x]
F[49,x] = 2*F[27,x]+F[41,x]+F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[47,x]
F[53,x] = F[50,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[19,x]+F[56,x]
F[56,x] = F[27,x]+F[44,x]+F[57,x]
F[57,x] = F[19,x]*F[4,x]
F[58,x] = F[134,x]+F[27,x]+F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[77,x]
F[61,x] = F[62,x]+F[7,x]
F[62,x] = F[27,x]+F[63,x]+F[68,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[11,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[4,x]+F[65,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[23,x]
F[71,x] = F[72,x]
F[72,x] = F[27,x]+F[32,x]+F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[23,x]
F[76,x] = F[72,x]
F[77,x] = F[104,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[7,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[11,x]
F[85,x] = F[78,x]+F[86,x]
F[86,x] = 2*F[27,x]+F[87,x]+F[91,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[87,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[96,x]+F[98,x]
F[96,x] = F[11,x]+F[97,x]
F[97,x] = F[83,x]
F[98,x] = F[93,x]+F[99,x]
F[99,x] = 2*F[27,x]+F[100,x]+F[91,x]
F[100,x] = F[101,x]*F[4,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = F[97,x]
F[103,x] = F[100,x]
F[104,x] = 2*F[27,x]+F[105,x]+F[131,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[107,x]+F[111,x]
F[107,x] = F[108,x]+F[62,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[4,x]
F[110,x] = F[65,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[105,x]
F[113,x] = 3*F[27,x]+F[114,x]+F[118,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[116,x]+F[117,x]
F[116,x] = F[108,x]
F[117,x] = F[114,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]
F[121,x] = F[122,x]*F[4,x]
F[122,x] = F[123,x]+F[125,x]
F[123,x] = F[124,x]+F[65,x]
F[124,x] = F[109,x]
F[125,x] = F[120,x]+F[126,x]
F[126,x] = 3*F[27,x]+F[118,x]+F[127,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[129,x]+F[130,x]
F[129,x] = F[124,x]
F[130,x] = F[127,x]
F[131,x] = F[132,x]*F[4,x]
F[132,x] = F[133,x]+F[93,x]
F[133,x] = F[121,x]
F[134,x] = F[135,x]*F[4,x]
F[135,x] = F[136,x]+F[161,x]
F[136,x] = F[137,x]+F[19,x]
F[137,x] = F[138,x]+F[158,x]+F[27,x]
F[138,x] = F[139,x]*F[4,x]
F[139,x] = F[140,x]+F[145,x]
F[140,x] = F[11,x]+F[141,x]
F[141,x] = F[142,x]+F[27,x]+F[63,x]
F[142,x] = F[143,x]*F[4,x]
F[143,x] = F[144,x]+F[23,x]
F[144,x] = F[142,x]+F[27,x]+F[32,x]
F[145,x] = F[146,x]+F[93,x]
F[146,x] = 2*F[27,x]+F[131,x]+F[147,x]
F[147,x] = F[148,x]*F[4,x]
F[148,x] = F[149,x]+F[151,x]
F[149,x] = F[141,x]+F[150,x]
F[150,x] = F[109,x]
F[151,x] = F[152,x]+F[153,x]
F[152,x] = F[147,x]
F[153,x] = 3*F[27,x]+F[118,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[150,x]
F[157,x] = F[154,x]
F[158,x] = F[159,x]*F[4,x]
F[159,x] = F[160,x]+F[19,x]
F[160,x] = F[158,x]+F[27,x]+F[44,x]
F[161,x] = F[162,x]
F[162,x] = F[163,x]+F[27,x]+F[28,x]
F[163,x] = F[164,x]*F[4,x]
F[164,x] = F[165,x]+F[55,x]
F[165,x] = F[162,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_{18}\! \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_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{58}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{19}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{54}\! \left(x \right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{30}\! \left(x \right) = F_{23}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{28}\! \left(x \right)
F_{36}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{37}\! \left(x \right)+F_{41}\! \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_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{31}\! \left(x \right)
F_{40}\! \left(x \right) = F_{37}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{48}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{32}\! \left(x \right)
F_{48}\! \left(x \right) = F_{43}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{41}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{47}\! \left(x \right)
F_{53}\! \left(x \right) = F_{50}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{19}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{27}\! \left(x \right)+F_{44}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{58}\! \left(x \right) = F_{134}\! \left(x \right)+F_{27}\! \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_{77}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{7}\! \left(x \right)
F_{62}\! \left(x \right) = F_{27}\! \left(x \right)+F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \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) = F_{4}\! \left(x \right)+F_{65}\! \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_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{23}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{27}\! \left(x \right)+F_{32}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{23}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{104}\! \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_{7}\! \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_{11}\! \left(x \right)
F_{85}\! \left(x \right) = F_{78}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{87}\! \left(x \right)+F_{91}\! \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_{87}\! \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_{96}\! \left(x \right)+F_{98}\! \left(x \right)
F_{96}\! \left(x \right) = F_{11}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{83}\! \left(x \right)
F_{98}\! \left(x \right) = F_{93}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{100}\! \left(x \right)+F_{91}\! \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_{103}\! \left(x \right)
F_{102}\! \left(x \right) = F_{97}\! \left(x \right)
F_{103}\! \left(x \right) = F_{100}\! \left(x \right)
F_{104}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{105}\! \left(x \right)+F_{131}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{111}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{62}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{4}\! \left(x \right)
F_{110}\! \left(x \right) = F_{65}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{105}\! \left(x \right)
F_{113}\! \left(x \right) = 3 F_{27}\! \left(x \right)+F_{114}\! \left(x \right)+F_{118}\! \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_{117}\! \left(x \right)
F_{116}\! \left(x \right) = F_{108}\! \left(x \right)
F_{117}\! \left(x \right) = F_{114}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{4}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{125}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{65}\! \left(x \right)
F_{124}\! \left(x \right) = F_{109}\! \left(x \right)
F_{125}\! \left(x \right) = F_{120}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = 3 F_{27}\! \left(x \right)+F_{118}\! \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_{130}\! \left(x \right)
F_{129}\! \left(x \right) = F_{124}\! \left(x \right)
F_{130}\! \left(x \right) = F_{127}\! \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_{93}\! \left(x \right)
F_{133}\! \left(x \right) = F_{121}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{4}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{161}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{19}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{158}\! \left(x \right)+F_{27}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{4}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{145}\! \left(x \right)
F_{140}\! \left(x \right) = F_{11}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{27}\! \left(x \right)+F_{63}\! \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_{23}\! \left(x \right)
F_{144}\! \left(x \right) = F_{142}\! \left(x \right)+F_{27}\! \left(x \right)+F_{32}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{93}\! \left(x \right)
F_{146}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{131}\! \left(x \right)+F_{147}\! \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_{151}\! \left(x \right)
F_{149}\! \left(x \right) = F_{141}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{109}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{153}\! \left(x \right)
F_{152}\! \left(x \right) = F_{147}\! \left(x \right)
F_{153}\! \left(x \right) = 3 F_{27}\! \left(x \right)+F_{118}\! \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_{150}\! \left(x \right)
F_{157}\! \left(x \right) = F_{154}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{4}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{19}\! \left(x \right)
F_{160}\! \left(x \right) = F_{158}\! \left(x \right)+F_{27}\! \left(x \right)+F_{44}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{27}\! \left(x \right)+F_{28}\! \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_{55}\! \left(x \right)
F_{165}\! \left(x \right) = F_{162}\! \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_18(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))
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_1(x) + F_4(x))
Eq(F_17(x), F_14(x))
Eq(F_18(x), F_19(x) + F_58(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_16(x)*F_4(x))
Eq(F_25(x), F_19(x) + F_26(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_54(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_34(x))
Eq(F_30(x), F_23(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_4(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_28(x))
Eq(F_36(x), 2*F_27(x) + F_37(x) + F_41(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_31(x))
Eq(F_40(x), F_37(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_48(x))
Eq(F_46(x), F_4(x) + F_47(x))
Eq(F_47(x), F_32(x))
Eq(F_48(x), F_43(x) + F_49(x))
Eq(F_49(x), 2*F_27(x) + F_41(x) + F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_47(x))
Eq(F_53(x), F_50(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_19(x) + F_56(x))
Eq(F_56(x), F_27(x) + F_44(x) + F_57(x))
Eq(F_57(x), F_19(x)*F_4(x))
Eq(F_58(x), F_134(x) + F_27(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_77(x))
Eq(F_61(x), F_62(x) + F_7(x))
Eq(F_62(x), F_27(x) + F_63(x) + F_68(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_11(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_4(x) + F_65(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_23(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_27(x) + F_32(x) + F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_23(x))
Eq(F_76(x), F_72(x))
Eq(F_77(x), F_104(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_7(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_11(x))
Eq(F_85(x), F_78(x) + F_86(x))
Eq(F_86(x), 2*F_27(x) + F_87(x) + F_91(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_87(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_96(x) + F_98(x))
Eq(F_96(x), F_11(x) + F_97(x))
Eq(F_97(x), F_83(x))
Eq(F_98(x), F_93(x) + F_99(x))
Eq(F_99(x), F_100(x) + 2*F_27(x) + F_91(x))
Eq(F_100(x), F_101(x)*F_4(x))
Eq(F_101(x), F_102(x) + F_103(x))
Eq(F_102(x), F_97(x))
Eq(F_103(x), F_100(x))
Eq(F_104(x), F_105(x) + F_131(x) + 2*F_27(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_107(x) + F_111(x))
Eq(F_107(x), F_108(x) + F_62(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_4(x))
Eq(F_110(x), F_65(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_105(x))
Eq(F_113(x), F_114(x) + F_118(x) + 3*F_27(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_116(x) + F_117(x))
Eq(F_116(x), F_108(x))
Eq(F_117(x), F_114(x))
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_122(x)*F_4(x))
Eq(F_122(x), F_123(x) + F_125(x))
Eq(F_123(x), F_124(x) + F_65(x))
Eq(F_124(x), F_109(x))
Eq(F_125(x), F_120(x) + F_126(x))
Eq(F_126(x), F_118(x) + F_127(x) + 3*F_27(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_129(x) + F_130(x))
Eq(F_129(x), F_124(x))
Eq(F_130(x), F_127(x))
Eq(F_131(x), F_132(x)*F_4(x))
Eq(F_132(x), F_133(x) + F_93(x))
Eq(F_133(x), F_121(x))
Eq(F_134(x), F_135(x)*F_4(x))
Eq(F_135(x), F_136(x) + F_161(x))
Eq(F_136(x), F_137(x) + F_19(x))
Eq(F_137(x), F_138(x) + F_158(x) + F_27(x))
Eq(F_138(x), F_139(x)*F_4(x))
Eq(F_139(x), F_140(x) + F_145(x))
Eq(F_140(x), F_11(x) + F_141(x))
Eq(F_141(x), F_142(x) + F_27(x) + F_63(x))
Eq(F_142(x), F_143(x)*F_4(x))
Eq(F_143(x), F_144(x) + F_23(x))
Eq(F_144(x), F_142(x) + F_27(x) + F_32(x))
Eq(F_145(x), F_146(x) + F_93(x))
Eq(F_146(x), F_131(x) + F_147(x) + 2*F_27(x))
Eq(F_147(x), F_148(x)*F_4(x))
Eq(F_148(x), F_149(x) + F_151(x))
Eq(F_149(x), F_141(x) + F_150(x))
Eq(F_150(x), F_109(x))
Eq(F_151(x), F_152(x) + F_153(x))
Eq(F_152(x), F_147(x))
Eq(F_153(x), F_118(x) + F_154(x) + 3*F_27(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_150(x))
Eq(F_157(x), F_154(x))
Eq(F_158(x), F_159(x)*F_4(x))
Eq(F_159(x), F_160(x) + F_19(x))
Eq(F_160(x), F_158(x) + F_27(x) + F_44(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_163(x) + F_27(x) + F_28(x))
Eq(F_163(x), F_164(x)*F_4(x))
Eq(F_164(x), F_165(x) + F_55(x))
Eq(F_165(x), F_162(x))
Pack JSON:
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Specification JSON:
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