0123_0321_1230_1302_2130
Counting sequence:
1, 1, 2, 6, 19, 50, 117, 263, 571, 1210, 2520, 5176, 10515, 21170, 42303, 83997, 165879, 326038, 638190, 1244650, 2419555, 4689890, 9066809, 17487139, 33654931, 64643570, 123942308, 237243260, 453422947, 865361442, 1649376835, 3139857145, 5970393455, 11340470574, 21519058266, 40794900558, 77268587891, 146230020562, 276520119613, 522506971007, 986619438571, 1861723710122, 3510777870960, 6616488279232, 12462362052083, 23460295404882, 44140552390151, 83008655895445, 156027023595367, 293140604488134, 550503622539334, 1033380481695282, 1939025650962755, 3636947267070210, 6819101084913537, 12780860142244635, 23946479830584643, 44851546218582498, 83979348827905852, 157192514010763012, 294144115988275139, 550252287528151874, 1029061072293111691, 1923986646207692017, 3596237639894238431, 6720224317424399966, 12554854366819124402, 23449598680325197462, 43788304443078308307, 81749072688212445298, 152585200444302787333, 284740744484779778807, 531247724357157900699, 990962767567976430234, 1848131208340699200264, 3446083477218217474376, 6424488300291798101971, 11974935581898788807410, 22316792579574167354831, 41583045125143096263181, 77469119766207831426263, 144301417834060579015158, 268747218231517111675294, 500438198180618390059130, 931733372464270037633571, 1734479404949417969165090, 3228378572234225651481289, 6008126100578919299584531, 11179807041406500245956083, 20800397025434507418675154, 38694773193209732152898772, 71974328560699344553591436, 133859378416996856271563043, 248924154134997615049195362, 462842766015087374827951059, 860496757071220359319850473, 1599614714591929103392881231, 2973260638455392663861309326, 5525900006770460220261692938, 10268960694617479661720046302, 19081140972072104140055489843
Generating function in Maple syntax:
(3*x^8+5*x^7+4*x^6-3*x^5-7*x^4-2*x^3+2*x-1)/(x-1)/(x^3+x^2+x-1)^2
Generating function in latex syntax:
\frac{3 x^{8}+5 x^{7}+4 x^{6}-3 x^{5}-7 x^{4}-2 x^{3}+2 x -1}{\left(x -1\right) \left(x^{3}+x^{2}+x -1\right)^{2}}
Generating function in sympy syntax:
(3*x**8 + 5*x**7 + 4*x**6 - 3*x**5 - 7*x**4 - 2*x**3 + 2*x - 1)/((x - 1)*(x**3 + x**2 + x - 1)**2)
Implicit equation for the generating function in Maple syntax:
-(x-1)*(x^3+x^2+x-1)^2*F(x)+3*x^8+5*x^7+4*x^6-3*x^5-7*x^4-2*x^3+2*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right) \left(x^{3}+x^{2}+x -1\right)^{2} F \! \left(x \right)+3 x^{8}+5 x^{7}+4 x^{6}-3 x^{5}-7 x^{4}-2 x^{3}+2 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/11616*((-660*(I+1/3*3^(1/2))*(n+13/55)*11^(1/2)+792*(n+5/2)*(1+I*3^(1/2)))*(17+3*11^(1/2)*3^(1/2))^(1/3)+(-1023*(n-1264/341)*(I-1/3*3^(1/2))*11^(1/2)+2079*(I*3^(1/2)-1)*(n-24/7))*(17+3*11^(1/2)*3^(1/2))^(2/3)+2112*n-2904)*(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)+1/11616*((660*(n+13/55)*(I-1/3*3^(1/2))*11^(1/2)-792*(n+5/2)*(I*3^(1/2)-1))*(17+3*11^(1/2)*3^(1/2))^(1/3)+(1023*(n-1264/341)*(I+1/3*3^(1/2))*11^(1/2)-2079*(n-24/7)*(1+I*3^(1/2)))*(17+3*11^(1/2)*3^(1/2))^(2/3)+2112*n-2904)*(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)-1/4+1/11616*(((440*n+104)*3^(1/2)*11^(1/2)-1584*n-3960)*(17+3*11^(1/2)*3^(1/2))^(1/3)+((-682*n+2528)*3^(1/2)*11^(1/2)+4158*n-14256)*(17+3*11^(1/2)*3^(1/2))^(2/3)+2112*n-2904)*(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))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(\left(-660 \left(\mathrm{I}+\frac{\sqrt{3}}{3}\right) \left(n +\frac{13}{55}\right) \sqrt{11}+792 \left(n +\frac{5}{2}\right) \left(1+\mathrm{I} \sqrt{3}\right)\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+\left(-1023 \left(n -\frac{1264}{341}\right) \left(\mathrm{I}-\frac{\sqrt{3}}{3}\right) \sqrt{11}+2079 \left(\mathrm{I} \sqrt{3}-1\right) \left(n -\frac{24}{7}\right)\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+2112 n -2904\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}}{11616}\\+\\\frac{\left(\left(660 \left(n +\frac{13}{55}\right) \left(\mathrm{I}-\frac{\sqrt{3}}{3}\right) \sqrt{11}-792 \left(n +\frac{5}{2}\right) \left(\mathrm{I} \sqrt{3}-1\right)\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+\left(1023 \left(n -\frac{1264}{341}\right) \left(\mathrm{I}+\frac{\sqrt{3}}{3}\right) \sqrt{11}-2079 \left(n -\frac{24}{7}\right) \left(1+\mathrm{I} \sqrt{3}\right)\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+2112 n -2904\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}}{11616}\\-\frac{1}{4}+\\\frac{\left(\left(\left(440 n +104\right) \sqrt{3}\, \sqrt{11}-1584 n -3960\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+\left(\left(-682 n +2528\right) \sqrt{3}\, \sqrt{11}+4158 n -14256\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+2112 n -2904\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}}{11616} & \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) = 50
a(6) = 117
a(7) = 263
a(8) = 571
a(n+2) = -1/3*a(n)-2/3*a(n+1)+1/3*a(n+4)+2/3*a(n+5)-1/3*a(n+6)-1/3, n >= 9
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) = 50
a \! \left(6\right) = 117
a \! \left(7\right) = 263
a \! \left(8\right) = 571
a \! \left(n +2\right) = -\frac{a \! \left(n \right)}{3}-\frac{2 a \! \left(n +1\right)}{3}+\frac{a \! \left(n +4\right)}{3}+\frac{2 a \! \left(n +5\right)}{3}-\frac{a \! \left(n +6\right)}{3}-\frac{1}{3}, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17754/
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[26,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]+F[19,x]+F[24,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[11,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[4,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[15,x]
F[26,x] = F[2,x]+F[27,x]
F[27,x] = F[18,x]+F[225,x]+F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[46,x]
F[30,x] = F[31,x]+F[7,x]
F[31,x] = F[18,x]+F[32,x]+F[43,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[36,x]
F[34,x] = F[11,x]+F[35,x]
F[35,x] = F[22,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[11,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[35,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[15,x]+F[37,x]
F[46,x] = F[112,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[56,x]
F[50,x] = F[51,x]+F[7,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[11,x]
F[55,x] = F[37,x]
F[56,x] = F[47,x]+F[57,x]
F[57,x] = 2*F[18,x]+F[58,x]+F[79,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[64,x]
F[60,x] = F[51,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[37,x]
F[64,x] = F[65,x]+F[70,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[51,x]
F[69,x] = F[65,x]
F[70,x] = F[71,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = F[61,x]
F[74,x] = F[75,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[61,x]
F[78,x] = F[75,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[108,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[87,x]
F[85,x] = F[11,x]+F[86,x]
F[86,x] = F[52,x]
F[87,x] = F[82,x]+F[88,x]
F[88,x] = 2*F[18,x]+F[79,x]+F[89,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[91,x]+F[93,x]
F[91,x] = F[86,x]+F[92,x]
F[92,x] = F[62,x]
F[93,x] = F[94,x]+F[99,x]
F[94,x] = F[95,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[97,x]+F[98,x]
F[97,x] = F[86,x]
F[98,x] = F[94,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[4,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = F[92,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[92,x]
F[107,x] = F[104,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[82,x]
F[112,x] = 2*F[18,x]+F[113,x]+F[218,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[115,x]+F[127,x]
F[115,x] = F[116,x]+F[31,x]
F[116,x] = 2*F[18,x]+F[117,x]+F[124,x]
F[117,x] = F[118,x]*F[4,x]
F[118,x] = F[119,x]+F[120,x]
F[119,x] = F[35,x]
F[120,x] = F[121,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[35,x]
F[124,x] = F[125,x]*F[4,x]
F[125,x] = F[126,x]
F[126,x] = F[121,x]+F[37,x]
F[127,x] = F[128,x]+F[192,x]
F[128,x] = F[129,x]
F[129,x] = F[130,x]*F[4,x]
F[130,x] = F[131,x]+F[137,x]
F[131,x] = F[132,x]+F[31,x]
F[132,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[35,x]
F[136,x] = F[121,x]
F[137,x] = F[128,x]+F[138,x]
F[138,x] = 3*F[18,x]+F[139,x]+F[160,x]
F[139,x] = F[140,x]*F[4,x]
F[140,x] = F[141,x]+F[145,x]
F[141,x] = F[132,x]+F[142,x]
F[142,x] = F[143,x]
F[143,x] = F[144,x]*F[4,x]
F[144,x] = F[121,x]
F[145,x] = F[146,x]+F[151,x]
F[146,x] = F[147,x]
F[147,x] = F[148,x]*F[4,x]
F[148,x] = F[149,x]+F[150,x]
F[149,x] = F[132,x]
F[150,x] = F[146,x]
F[151,x] = F[152,x]
F[152,x] = F[153,x]*F[4,x]
F[153,x] = F[154,x]+F[155,x]
F[154,x] = F[142,x]
F[155,x] = F[156,x]
F[156,x] = F[157,x]*F[4,x]
F[157,x] = F[158,x]+F[159,x]
F[158,x] = F[142,x]
F[159,x] = F[156,x]
F[160,x] = F[161,x]*F[4,x]
F[161,x] = F[162,x]+F[189,x]
F[162,x] = F[163,x]
F[163,x] = F[164,x]
F[164,x] = F[165,x]*F[4,x]
F[165,x] = F[166,x]+F[168,x]
F[166,x] = F[167,x]+F[35,x]
F[167,x] = F[133,x]
F[168,x] = F[163,x]+F[169,x]
F[169,x] = 3*F[18,x]+F[160,x]+F[170,x]
F[170,x] = F[171,x]*F[4,x]
F[171,x] = F[172,x]+F[174,x]
F[172,x] = F[167,x]+F[173,x]
F[173,x] = F[143,x]
F[174,x] = F[175,x]+F[180,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[167,x]
F[179,x] = F[175,x]
F[180,x] = F[181,x]
F[181,x] = F[182,x]*F[4,x]
F[182,x] = F[183,x]+F[184,x]
F[183,x] = F[173,x]
F[184,x] = F[185,x]
F[185,x] = F[186,x]*F[4,x]
F[186,x] = F[187,x]+F[188,x]
F[187,x] = F[173,x]
F[188,x] = F[185,x]
F[189,x] = F[190,x]
F[190,x] = F[191,x]*F[4,x]
F[191,x] = F[163,x]
F[192,x] = 3*F[18,x]+F[193,x]+F[214,x]
F[193,x] = F[194,x]*F[4,x]
F[194,x] = F[195,x]+F[199,x]
F[195,x] = F[116,x]+F[196,x]
F[196,x] = F[197,x]
F[197,x] = F[198,x]*F[4,x]
F[198,x] = F[121,x]
F[199,x] = F[200,x]+F[205,x]
F[200,x] = F[201,x]
F[201,x] = F[202,x]*F[4,x]
F[202,x] = F[203,x]+F[204,x]
F[203,x] = F[116,x]
F[204,x] = F[200,x]
F[205,x] = F[206,x]
F[206,x] = F[207,x]*F[4,x]
F[207,x] = F[208,x]+F[209,x]
F[208,x] = F[196,x]
F[209,x] = F[210,x]
F[210,x] = F[211,x]*F[4,x]
F[211,x] = F[212,x]+F[213,x]
F[212,x] = F[196,x]
F[213,x] = F[210,x]
F[214,x] = F[215,x]*F[4,x]
F[215,x] = F[216,x]+F[217,x]
F[216,x] = F[163,x]
F[217,x] = F[190,x]
F[218,x] = F[219,x]*F[4,x]
F[219,x] = F[220,x]+F[221,x]
F[220,x] = F[163,x]+F[82,x]
F[221,x] = F[109,x]+F[222,x]
F[222,x] = F[223,x]
F[223,x] = F[224,x]*F[4,x]
F[224,x] = F[163,x]
F[225,x] = F[226,x]*F[4,x]
F[226,x] = F[227,x]+F[228,x]
F[227,x] = F[2,x]+F[82,x]
F[228,x] = F[229,x]+F[232,x]
F[229,x] = F[230,x]
F[230,x] = F[231,x]*F[4,x]
F[231,x] = F[2,x]
F[232,x] = F[233,x]
F[233,x] = F[234,x]*F[4,x]
F[234,x] = F[82,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_{26}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{24}\! \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_{11}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right)
F_{26}\! \left(x \right) = F_{2}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right)+F_{225}\! \left(x \right)+F_{28}\! \left(x \right)
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_{46}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{7}\! \left(x \right)
F_{31}\! \left(x \right) = F_{18}\! \left(x \right)+F_{32}\! \left(x \right)+F_{43}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{22}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{11}\! \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_{35}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{15}\! \left(x \right)+F_{37}\! \left(x \right)
F_{46}\! \left(x \right) = F_{112}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \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_{56}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{7}\! \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_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{11}\! \left(x \right)
F_{55}\! \left(x \right) = F_{37}\! \left(x \right)
F_{56}\! \left(x \right) = F_{47}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{58}\! \left(x \right)+F_{79}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{64}\! \left(x \right)
F_{60}\! \left(x \right) = F_{51}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \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_{37}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{70}\! \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_{51}\! \left(x \right)
F_{69}\! \left(x \right) = F_{65}\! \left(x \right)
F_{70}\! \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_{74}\! \left(x \right)
F_{73}\! \left(x \right) = F_{61}\! \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_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{61}\! \left(x \right)
F_{78}\! \left(x \right) = F_{75}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{108}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \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_{85}\! \left(x \right)+F_{87}\! \left(x \right)
F_{85}\! \left(x \right) = F_{11}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{52}\! \left(x \right)
F_{87}\! \left(x \right) = F_{82}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{79}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{93}\! \left(x \right)
F_{91}\! \left(x \right) = F_{86}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{62}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{99}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \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_{98}\! \left(x \right)
F_{97}\! \left(x \right) = F_{86}\! \left(x \right)
F_{98}\! \left(x \right) = F_{94}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \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_{92}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \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_{92}\! \left(x \right)
F_{107}\! \left(x \right) = F_{104}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{82}\! \left(x \right)
F_{112}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{113}\! \left(x \right)+F_{218}\! \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_{127}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{31}\! \left(x \right)
F_{116}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{117}\! \left(x \right)+F_{124}\! \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_{35}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{4}\! \left(x \right)
F_{123}\! \left(x \right) = F_{35}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{4}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{121}\! \left(x \right)+F_{37}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{192}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \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_{137}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{31}\! \left(x \right)
F_{132}\! \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_{35}\! \left(x \right)
F_{136}\! \left(x \right) = F_{121}\! \left(x \right)
F_{137}\! \left(x \right) = F_{128}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{139}\! \left(x \right)+F_{160}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{145}\! \left(x \right)
F_{141}\! \left(x \right) = F_{132}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{4}\! \left(x \right)
F_{144}\! \left(x \right) = F_{121}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{151}\! \left(x \right)
F_{146}\! \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_{150}\! \left(x \right)
F_{149}\! \left(x \right) = F_{132}\! \left(x \right)
F_{150}\! \left(x \right) = F_{146}\! \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_{155}\! \left(x \right)
F_{154}\! \left(x \right) = F_{142}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \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_{159}\! \left(x \right)
F_{158}\! \left(x \right) = F_{142}\! \left(x \right)
F_{159}\! \left(x \right) = F_{156}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{4}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{189}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right) F_{4}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{168}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{35}\! \left(x \right)
F_{167}\! \left(x \right) = F_{133}\! \left(x \right)
F_{168}\! \left(x \right) = F_{163}\! \left(x \right)+F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{160}\! \left(x \right)+F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{4}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{174}\! \left(x \right)
F_{172}\! \left(x \right) = F_{167}\! \left(x \right)+F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{143}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{180}\! \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_{167}\! \left(x \right)
F_{179}\! \left(x \right) = F_{175}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \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_{184}\! \left(x \right)
F_{183}\! \left(x \right) = F_{173}\! \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_{187}\! \left(x \right)+F_{188}\! \left(x \right)
F_{187}\! \left(x \right) = F_{173}\! \left(x \right)
F_{188}\! \left(x \right) = F_{185}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right) F_{4}\! \left(x \right)
F_{191}\! \left(x \right) = F_{163}\! \left(x \right)
F_{192}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{193}\! \left(x \right)+F_{214}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right) F_{4}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)+F_{199}\! \left(x \right)
F_{195}\! \left(x \right) = F_{116}\! \left(x \right)+F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right) F_{4}\! \left(x \right)
F_{198}\! \left(x \right) = F_{121}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)+F_{205}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right) F_{4}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)+F_{204}\! \left(x \right)
F_{203}\! \left(x \right) = F_{116}\! \left(x \right)
F_{204}\! \left(x \right) = F_{200}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right) F_{4}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{209}\! \left(x \right)
F_{208}\! \left(x \right) = F_{196}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right) F_{4}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{213}\! \left(x \right)
F_{212}\! \left(x \right) = F_{196}\! \left(x \right)
F_{213}\! \left(x \right) = F_{210}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right) F_{4}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right)+F_{217}\! \left(x \right)
F_{216}\! \left(x \right) = F_{163}\! \left(x \right)
F_{217}\! \left(x \right) = F_{190}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right) F_{4}\! \left(x \right)
F_{219}\! \left(x \right) = F_{220}\! \left(x \right)+F_{221}\! \left(x \right)
F_{220}\! \left(x \right) = F_{163}\! \left(x \right)+F_{82}\! \left(x \right)
F_{221}\! \left(x \right) = F_{109}\! \left(x \right)+F_{222}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right) F_{4}\! \left(x \right)
F_{224}\! \left(x \right) = F_{163}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right) F_{4}\! \left(x \right)
F_{226}\! \left(x \right) = F_{227}\! \left(x \right)+F_{228}\! \left(x \right)
F_{227}\! \left(x \right) = F_{2}\! \left(x \right)+F_{82}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right)+F_{232}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right) F_{4}\! \left(x \right)
F_{231}\! \left(x \right) = F_{2}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right) F_{4}\! \left(x \right)
F_{234}\! \left(x \right) = F_{82}\! \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_26(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_24(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_11(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_4(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_15(x))
Eq(F_26(x), F_2(x) + F_27(x))
Eq(F_27(x), F_18(x) + F_225(x) + F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_46(x))
Eq(F_30(x), F_31(x) + F_7(x))
Eq(F_31(x), F_18(x) + F_32(x) + F_43(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_36(x))
Eq(F_34(x), F_11(x) + F_35(x))
Eq(F_35(x), F_22(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_11(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_35(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_15(x) + F_37(x))
Eq(F_46(x), F_112(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_56(x))
Eq(F_50(x), F_51(x) + F_7(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_11(x))
Eq(F_55(x), F_37(x))
Eq(F_56(x), F_47(x) + F_57(x))
Eq(F_57(x), 2*F_18(x) + F_58(x) + F_79(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_64(x))
Eq(F_60(x), F_51(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_37(x))
Eq(F_64(x), F_65(x) + F_70(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_51(x))
Eq(F_69(x), F_65(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), F_61(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_61(x))
Eq(F_78(x), F_75(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_108(x) + F_81(x))
Eq(F_81(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_85(x) + F_87(x))
Eq(F_85(x), F_11(x) + F_86(x))
Eq(F_86(x), F_52(x))
Eq(F_87(x), F_82(x) + F_88(x))
Eq(F_88(x), 2*F_18(x) + F_79(x) + F_89(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_93(x))
Eq(F_91(x), F_86(x) + F_92(x))
Eq(F_92(x), F_62(x))
Eq(F_93(x), F_94(x) + F_99(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_97(x) + F_98(x))
Eq(F_97(x), F_86(x))
Eq(F_98(x), F_94(x))
Eq(F_99(x), F_100(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_92(x))
Eq(F_103(x), F_104(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_92(x))
Eq(F_107(x), F_104(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_82(x))
Eq(F_112(x), F_113(x) + 2*F_18(x) + F_218(x))
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_115(x) + F_127(x))
Eq(F_115(x), F_116(x) + F_31(x))
Eq(F_116(x), F_117(x) + F_124(x) + 2*F_18(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_35(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_35(x))
Eq(F_124(x), F_125(x)*F_4(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_121(x) + F_37(x))
Eq(F_127(x), F_128(x) + F_192(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x)*F_4(x))
Eq(F_130(x), F_131(x) + F_137(x))
Eq(F_131(x), F_132(x) + F_31(x))
Eq(F_132(x), F_133(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_35(x))
Eq(F_136(x), F_121(x))
Eq(F_137(x), F_128(x) + F_138(x))
Eq(F_138(x), F_139(x) + F_160(x) + 3*F_18(x))
Eq(F_139(x), F_140(x)*F_4(x))
Eq(F_140(x), F_141(x) + F_145(x))
Eq(F_141(x), F_132(x) + F_142(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_144(x)*F_4(x))
Eq(F_144(x), F_121(x))
Eq(F_145(x), F_146(x) + F_151(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_148(x)*F_4(x))
Eq(F_148(x), F_149(x) + F_150(x))
Eq(F_149(x), F_132(x))
Eq(F_150(x), F_146(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_155(x))
Eq(F_154(x), F_142(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_157(x)*F_4(x))
Eq(F_157(x), F_158(x) + F_159(x))
Eq(F_158(x), F_142(x))
Eq(F_159(x), F_156(x))
Eq(F_160(x), F_161(x)*F_4(x))
Eq(F_161(x), F_162(x) + F_189(x))
Eq(F_162(x), F_163(x))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_165(x)*F_4(x))
Eq(F_165(x), F_166(x) + F_168(x))
Eq(F_166(x), F_167(x) + F_35(x))
Eq(F_167(x), F_133(x))
Eq(F_168(x), F_163(x) + F_169(x))
Eq(F_169(x), F_160(x) + F_170(x) + 3*F_18(x))
Eq(F_170(x), F_171(x)*F_4(x))
Eq(F_171(x), F_172(x) + F_174(x))
Eq(F_172(x), F_167(x) + F_173(x))
Eq(F_173(x), F_143(x))
Eq(F_174(x), F_175(x) + F_180(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_167(x))
Eq(F_179(x), F_175(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_182(x)*F_4(x))
Eq(F_182(x), F_183(x) + F_184(x))
Eq(F_183(x), F_173(x))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_186(x)*F_4(x))
Eq(F_186(x), F_187(x) + F_188(x))
Eq(F_187(x), F_173(x))
Eq(F_188(x), F_185(x))
Eq(F_189(x), F_190(x))
Eq(F_190(x), F_191(x)*F_4(x))
Eq(F_191(x), F_163(x))
Eq(F_192(x), 3*F_18(x) + F_193(x) + F_214(x))
Eq(F_193(x), F_194(x)*F_4(x))
Eq(F_194(x), F_195(x) + F_199(x))
Eq(F_195(x), F_116(x) + F_196(x))
Eq(F_196(x), F_197(x))
Eq(F_197(x), F_198(x)*F_4(x))
Eq(F_198(x), F_121(x))
Eq(F_199(x), F_200(x) + F_205(x))
Eq(F_200(x), F_201(x))
Eq(F_201(x), F_202(x)*F_4(x))
Eq(F_202(x), F_203(x) + F_204(x))
Eq(F_203(x), F_116(x))
Eq(F_204(x), F_200(x))
Eq(F_205(x), F_206(x))
Eq(F_206(x), F_207(x)*F_4(x))
Eq(F_207(x), F_208(x) + F_209(x))
Eq(F_208(x), F_196(x))
Eq(F_209(x), F_210(x))
Eq(F_210(x), F_211(x)*F_4(x))
Eq(F_211(x), F_212(x) + F_213(x))
Eq(F_212(x), F_196(x))
Eq(F_213(x), F_210(x))
Eq(F_214(x), F_215(x)*F_4(x))
Eq(F_215(x), F_216(x) + F_217(x))
Eq(F_216(x), F_163(x))
Eq(F_217(x), F_190(x))
Eq(F_218(x), F_219(x)*F_4(x))
Eq(F_219(x), F_220(x) + F_221(x))
Eq(F_220(x), F_163(x) + F_82(x))
Eq(F_221(x), F_109(x) + F_222(x))
Eq(F_222(x), F_223(x))
Eq(F_223(x), F_224(x)*F_4(x))
Eq(F_224(x), F_163(x))
Eq(F_225(x), F_226(x)*F_4(x))
Eq(F_226(x), F_227(x) + F_228(x))
Eq(F_227(x), F_2(x) + F_82(x))
Eq(F_228(x), F_229(x) + F_232(x))
Eq(F_229(x), F_230(x))
Eq(F_230(x), F_231(x)*F_4(x))
Eq(F_231(x), F_2(x))
Eq(F_232(x), F_233(x))
Eq(F_233(x), F_234(x)*F_4(x))
Eq(F_234(x), F_82(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", 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