0123_0231_2130_3021
Counting sequence:
1, 1, 2, 6, 20, 59, 139, 290, 569, 1082, 2026, 3765, 6972, 12891, 23819, 43996, 81245, 149994, 276844, 510825, 942284, 1737665, 3203543, 5904504, 10880127, 20044346, 36920428, 67993515, 125199480, 230504497, 424331177, 781061492, 1437558935, 2645641632, 4868615960, 8958862751, 16484522962, 30330453217, 55803696009, 102666983950, 188879305387, 347476472928, 639227425914, 1175914359571, 2163154081778, 3979162850615, 7319634103605, 13464220836202, 24766690407773, 45556487770944, 83797014061754, 154135749717109, 283514424080046, 521487917872887, 959203994221703, 1764312968748070, 3245177415975909, 5968973546660886, 10978915634242214, 20193797467460841, 37142869221812792, 68317495767556599, 125657258474330311, 231122632925251424, 425105492646201449, 781898498986409766, 1438147844977564520, 2645186171970516829, 4865288071714547176, 8948711979803039229, 16459331670408584019, 30273567059987076412, 55681991495180101419, 102415506348618085078, 188372061811809003880, 346471172686673271071, 637261350786190198708, 1172108808254828410573, 2155848164636937674021, 3965229379557358032504, 7293204241237771679139, 13414310730100116716636, 24672791184351943341588, 45380381933814578002515, 83467606459848081260654, 153520977967720792091869, 282369287362671084064709, 519358391181233779637266, 955249496903907110747415, 1756978535231087251647484, 3231588623491784874208950, 5943820215585611246004487, 10932393134442872113464750, 20107811293613488984709715, 36984039723869581836842033, 68024268552246773178739502, 125116159050278283736706409, 230124531207263908732455868, 423265062171206675364515318, 778505919671035847530490217, 1431895783653211121040919434
Generating function in Maple syntax:
(2*x^12+3*x^11-5*x^10-15*x^9-12*x^8+4*x^7+17*x^6+2*x^5-x^4-x^3-5*x^2+4*x-1)/(x^2+x-1)/(x^3+x^2+x-1)/(x-1)^3
Generating function in latex syntax:
\frac{2 x^{12}+3 x^{11}-5 x^{10}-15 x^{9}-12 x^{8}+4 x^{7}+17 x^{6}+2 x^{5}-x^{4}-x^{3}-5 x^{2}+4 x -1}{\left(x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(2*x**12 + 3*x**11 - 5*x**10 - 15*x**9 - 12*x**8 + 4*x**7 + 17*x**6 + 2*x**5 - x**4 - x**3 - 5*x**2 + 4*x - 1)/((x - 1)**3*(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)^3*F(x)+2*x^12+3*x^11-5*x^10-15*x^9-12*x^8+4*x^7+17*x^6+2*x^5-x^4-x^3-5*x^2+4*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)^{3} F \! \left(x \right)+2 x^{12}+3 x^{11}-5 x^{10}-15 x^{9}-12 x^{8}+4 x^{7}+17 x^{6}+2 x^{5}-x^{4}-x^{3}-5 x^{2}+4 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,n = 2,2,n = 3,6,n = 4,20,1/2640*(((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*(528*5^(1/2)-2640)*(-1/2*5^(1/2)-1/2)^(-n)+1/2640*(-528*5^(1/2)-2640)*(1/2*5^(1/2)-1/2)^(-n)+2*n^2-37/2*n+14)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ 2 & n =2 \\ 6 & n =3 \\ 20 & 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(528 \sqrt{5}-2640\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{2640}+\frac{\left(-528 \sqrt{5}-2640\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{2640}+\\2 n^{2}-\frac{37 n}{2}+14 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 59
a(6) = 139
a(7) = 290
a(8) = 569
a(9) = 1082
a(10) = 2026
a(11) = 3765
a(12) = 6972
a(n+5) = 4*n^2+2*a(n+4)-a(n)-2*a(n+1)-a(n+2)+a(n+3)-45*n+45, n >= 13
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 59
a \! \left(6\right) = 139
a \! \left(7\right) = 290
a \! \left(8\right) = 569
a \! \left(9\right) = 1082
a \! \left(10\right) = 2026
a \! \left(11\right) = 3765
a \! \left(12\right) = 6972
a \! \left(n +5\right) = 4 n^{2}+2 a \! \left(n +4\right)-a \! \left(n \right)-2 a \! \left(n +1\right)-a \! \left(n +2\right)+a \! \left(n +3\right)-45 n +45, \quad n \geq 13
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15064/
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[29,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[24,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[4,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[4,x]
F[23,x] = F[19,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[11,x]
F[28,x] = F[24,x]
F[29,x] = F[30,x]+F[68,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[1,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[17,x]*F[4,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = F[38,x]+F[39,x]+F[64,x]
F[38,x] = 0
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[34,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[22,x]*F[4,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[39,x]
F[46,x] = 2*F[38,x]+F[47,x]+F[51,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[42,x]
F[50,x] = F[47,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[58,x]
F[56,x] = F[4,x]+F[57,x]
F[57,x] = F[43,x]
F[58,x] = F[53,x]+F[59,x]
F[59,x] = 2*F[38,x]+F[51,x]+F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[63,x]
F[62,x] = F[57,x]
F[63,x] = F[60,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[30,x]+F[66,x]
F[66,x] = F[38,x]+F[54,x]+F[67,x]
F[67,x] = F[30,x]*F[4,x]
F[68,x] = F[153,x]+F[38,x]+F[69,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]+F[99,x]
F[71,x] = F[7,x]+F[72,x]
F[72,x] = F[38,x]+F[73,x]+F[78,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[11,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[4,x]+F[75,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[34,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[27,x]*F[4,x]
F[83,x] = F[84,x]+F[94,x]
F[84,x] = F[38,x]+F[43,x]+F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[87,x]+F[88,x]
F[87,x] = F[34,x]+F[57,x]
F[88,x] = F[84,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = F[57,x]
F[93,x] = F[89,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[81,x]
F[98,x] = F[94,x]
F[99,x] = F[100,x]+F[123,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]+F[105,x]
F[103,x] = F[104,x]+F[7,x]
F[104,x] = F[82,x]
F[105,x] = F[100,x]+F[106,x]
F[106,x] = 2*F[38,x]+F[107,x]+F[111,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[104,x]
F[110,x] = F[107,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[116,x]+F[117,x]
F[116,x] = F[11,x]+F[81,x]
F[117,x] = F[113,x]+F[118,x]
F[118,x] = 2*F[38,x]+F[111,x]+F[119,x]
F[119,x] = F[120,x]*F[4,x]
F[120,x] = F[121,x]+F[122,x]
F[121,x] = F[81,x]
F[122,x] = F[119,x]
F[123,x] = 2*F[38,x]+F[124,x]+F[150,x]
F[124,x] = F[125,x]*F[4,x]
F[125,x] = F[126,x]+F[130,x]
F[126,x] = F[127,x]+F[72,x]
F[127,x] = F[128,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[75,x]
F[130,x] = F[131,x]+F[132,x]
F[131,x] = F[124,x]
F[132,x] = 3*F[38,x]+F[133,x]+F[137,x]
F[133,x] = F[134,x]*F[4,x]
F[134,x] = F[135,x]+F[136,x]
F[135,x] = F[127,x]
F[136,x] = F[133,x]
F[137,x] = F[138,x]*F[4,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]
F[140,x] = F[141,x]*F[4,x]
F[141,x] = F[142,x]+F[144,x]
F[142,x] = F[143,x]+F[75,x]
F[143,x] = F[128,x]
F[144,x] = F[139,x]+F[145,x]
F[145,x] = 3*F[38,x]+F[137,x]+F[146,x]
F[146,x] = F[147,x]*F[4,x]
F[147,x] = F[148,x]+F[149,x]
F[148,x] = F[143,x]
F[149,x] = F[146,x]
F[150,x] = F[151,x]*F[4,x]
F[151,x] = F[113,x]+F[152,x]
F[152,x] = F[140,x]
F[153,x] = F[154,x]*F[4,x]
F[154,x] = F[155,x]+F[180,x]
F[155,x] = F[156,x]+F[30,x]
F[156,x] = F[157,x]+F[177,x]+F[38,x]
F[157,x] = F[158,x]*F[4,x]
F[158,x] = F[159,x]+F[164,x]
F[159,x] = F[11,x]+F[160,x]
F[160,x] = F[161,x]+F[38,x]+F[73,x]
F[161,x] = F[162,x]*F[4,x]
F[162,x] = F[163,x]+F[34,x]
F[163,x] = F[161,x]+F[38,x]+F[43,x]
F[164,x] = F[113,x]+F[165,x]
F[165,x] = 2*F[38,x]+F[150,x]+F[166,x]
F[166,x] = F[167,x]*F[4,x]
F[167,x] = F[168,x]+F[170,x]
F[168,x] = F[160,x]+F[169,x]
F[169,x] = F[128,x]
F[170,x] = F[171,x]+F[172,x]
F[171,x] = F[166,x]
F[172,x] = 3*F[38,x]+F[137,x]+F[173,x]
F[173,x] = F[174,x]*F[4,x]
F[174,x] = F[175,x]+F[176,x]
F[175,x] = F[169,x]
F[176,x] = F[173,x]
F[177,x] = F[178,x]*F[4,x]
F[178,x] = F[179,x]+F[30,x]
F[179,x] = F[177,x]+F[38,x]+F[54,x]
F[180,x] = F[181,x]+F[190,x]
F[181,x] = F[182,x]+F[38,x]+F[39,x]
F[182,x] = F[183,x]*F[4,x]
F[183,x] = F[184,x]+F[65,x]
F[184,x] = F[181,x]+F[185,x]
F[185,x] = 2*F[38,x]+F[186,x]+F[60,x]
F[186,x] = F[187,x]*F[4,x]
F[187,x] = F[188,x]+F[52,x]
F[188,x] = F[189,x]
F[189,x] = 2*F[38,x]+F[186,x]+F[60,x]
F[190,x] = 2*F[38,x]+F[191,x]+F[195,x]
F[191,x] = F[192,x]*F[4,x]
F[192,x] = F[193,x]+F[194,x]
F[193,x] = F[81,x]
F[194,x] = F[119,x]
F[195,x] = F[196,x]*F[4,x]
F[196,x] = F[112,x]+F[197,x]
F[197,x] = F[198,x]
F[198,x] = 2*F[38,x]+F[119,x]+F[195,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_{29}\! \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_{24}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{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_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{68}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{1}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)+F_{64}\! \left(x \right)
F_{38}\! \left(x \right) = 0
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{39}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{47}\! \left(x \right)+F_{51}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{42}\! \left(x \right)
F_{50}\! \left(x \right) = F_{47}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{43}\! \left(x \right)
F_{58}\! \left(x \right) = F_{53}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{51}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{57}\! \left(x \right)
F_{63}\! \left(x \right) = F_{60}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{30}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{38}\! \left(x \right)+F_{54}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{68}\! \left(x \right) = F_{153}\! \left(x \right)+F_{38}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{99}\! \left(x \right)
F_{71}\! \left(x \right) = F_{7}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{38}\! \left(x \right)+F_{73}\! \left(x \right)+F_{78}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{11}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right)+F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{34}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{94}\! \left(x \right)
F_{84}\! \left(x \right) = F_{38}\! \left(x \right)+F_{43}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{88}\! \left(x \right)
F_{87}\! \left(x \right) = F_{34}\! \left(x \right)+F_{57}\! \left(x \right)
F_{88}\! \left(x \right) = F_{84}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{92}\! \left(x \right) = F_{57}\! \left(x \right)
F_{93}\! \left(x \right) = F_{89}\! \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_{81}\! \left(x \right)
F_{98}\! \left(x \right) = F_{94}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{123}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{105}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{7}\! \left(x \right)
F_{104}\! \left(x \right) = F_{82}\! \left(x \right)
F_{105}\! \left(x \right) = F_{100}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{107}\! \left(x \right)+F_{111}\! \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_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{104}\! \left(x \right)
F_{110}\! \left(x \right) = F_{107}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \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_{11}\! \left(x \right)+F_{81}\! \left(x \right)
F_{117}\! \left(x \right) = F_{113}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{111}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{4}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{81}\! \left(x \right)
F_{122}\! \left(x \right) = F_{119}\! \left(x \right)
F_{123}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{124}\! \left(x \right)+F_{150}\! \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_{130}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{72}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = F_{75}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)
F_{131}\! \left(x \right) = F_{124}\! \left(x \right)
F_{132}\! \left(x \right) = 3 F_{38}\! \left(x \right)+F_{133}\! \left(x \right)+F_{137}\! \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_{127}\! \left(x \right)
F_{136}\! \left(x \right) = F_{133}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{4}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{144}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{75}\! \left(x \right)
F_{143}\! \left(x \right) = F_{128}\! \left(x \right)
F_{144}\! \left(x \right) = F_{139}\! \left(x \right)+F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = 3 F_{38}\! \left(x \right)+F_{137}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right) F_{4}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{149}\! \left(x \right)
F_{148}\! \left(x \right) = F_{143}\! \left(x \right)
F_{149}\! \left(x \right) = F_{146}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right) F_{4}\! \left(x \right)
F_{151}\! \left(x \right) = F_{113}\! \left(x \right)+F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{140}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{4}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{180}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{30}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{177}\! \left(x \right)+F_{38}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{4}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{164}\! \left(x \right)
F_{159}\! \left(x \right) = F_{11}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{38}\! \left(x \right)+F_{73}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right) F_{4}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{34}\! \left(x \right)
F_{163}\! \left(x \right) = F_{161}\! \left(x \right)+F_{38}\! \left(x \right)+F_{43}\! \left(x \right)
F_{164}\! \left(x \right) = F_{113}\! \left(x \right)+F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{150}\! \left(x \right)+F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right) F_{4}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{170}\! \left(x \right)
F_{168}\! \left(x \right) = F_{160}\! \left(x \right)+F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{128}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)+F_{172}\! \left(x \right)
F_{171}\! \left(x \right) = F_{166}\! \left(x \right)
F_{172}\! \left(x \right) = 3 F_{38}\! \left(x \right)+F_{137}\! \left(x \right)+F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right) F_{4}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{176}\! \left(x \right)
F_{175}\! \left(x \right) = F_{169}\! \left(x \right)
F_{176}\! \left(x \right) = F_{173}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right) F_{4}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)+F_{30}\! \left(x \right)
F_{179}\! \left(x \right) = F_{177}\! \left(x \right)+F_{38}\! \left(x \right)+F_{54}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{190}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right) F_{4}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{65}\! \left(x \right)
F_{184}\! \left(x \right) = F_{181}\! \left(x \right)+F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{186}\! \left(x \right)+F_{60}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right) F_{4}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{52}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{186}\! \left(x \right)+F_{60}\! \left(x \right)
F_{190}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{191}\! \left(x \right)+F_{195}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right) F_{4}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{194}\! \left(x \right)
F_{193}\! \left(x \right) = F_{81}\! \left(x \right)
F_{194}\! \left(x \right) = F_{119}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right) F_{4}\! \left(x \right)
F_{196}\! \left(x \right) = F_{112}\! \left(x \right)+F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{119}\! \left(x \right)+F_{195}\! \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_29(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_24(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_4(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_4(x))
Eq(F_23(x), F_19(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_11(x))
Eq(F_28(x), F_24(x))
Eq(F_29(x), F_30(x) + F_68(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_1(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_17(x)*F_4(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), F_38(x) + F_39(x) + F_64(x))
Eq(F_38(x), 0)
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_34(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_22(x)*F_4(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_39(x))
Eq(F_46(x), 2*F_38(x) + F_47(x) + F_51(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_42(x))
Eq(F_50(x), F_47(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_58(x))
Eq(F_56(x), F_4(x) + F_57(x))
Eq(F_57(x), F_43(x))
Eq(F_58(x), F_53(x) + F_59(x))
Eq(F_59(x), 2*F_38(x) + F_51(x) + F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_63(x))
Eq(F_62(x), F_57(x))
Eq(F_63(x), F_60(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_30(x) + F_66(x))
Eq(F_66(x), F_38(x) + F_54(x) + F_67(x))
Eq(F_67(x), F_30(x)*F_4(x))
Eq(F_68(x), F_153(x) + F_38(x) + F_69(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_99(x))
Eq(F_71(x), F_7(x) + F_72(x))
Eq(F_72(x), F_38(x) + F_73(x) + F_78(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_11(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_4(x) + F_75(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_34(x) + F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_27(x)*F_4(x))
Eq(F_83(x), F_84(x) + F_94(x))
Eq(F_84(x), F_38(x) + F_43(x) + F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_88(x))
Eq(F_87(x), F_34(x) + F_57(x))
Eq(F_88(x), F_84(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), F_57(x))
Eq(F_93(x), F_89(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_81(x))
Eq(F_98(x), F_94(x))
Eq(F_99(x), F_100(x) + F_123(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x) + F_105(x))
Eq(F_103(x), F_104(x) + F_7(x))
Eq(F_104(x), F_82(x))
Eq(F_105(x), F_100(x) + F_106(x))
Eq(F_106(x), F_107(x) + F_111(x) + 2*F_38(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_104(x))
Eq(F_110(x), F_107(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(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_11(x) + F_81(x))
Eq(F_117(x), F_113(x) + F_118(x))
Eq(F_118(x), F_111(x) + F_119(x) + 2*F_38(x))
Eq(F_119(x), F_120(x)*F_4(x))
Eq(F_120(x), F_121(x) + F_122(x))
Eq(F_121(x), F_81(x))
Eq(F_122(x), F_119(x))
Eq(F_123(x), F_124(x) + F_150(x) + 2*F_38(x))
Eq(F_124(x), F_125(x)*F_4(x))
Eq(F_125(x), F_126(x) + F_130(x))
Eq(F_126(x), F_127(x) + F_72(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_75(x))
Eq(F_130(x), F_131(x) + F_132(x))
Eq(F_131(x), F_124(x))
Eq(F_132(x), F_133(x) + F_137(x) + 3*F_38(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_127(x))
Eq(F_136(x), F_133(x))
Eq(F_137(x), F_138(x)*F_4(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_141(x)*F_4(x))
Eq(F_141(x), F_142(x) + F_144(x))
Eq(F_142(x), F_143(x) + F_75(x))
Eq(F_143(x), F_128(x))
Eq(F_144(x), F_139(x) + F_145(x))
Eq(F_145(x), F_137(x) + F_146(x) + 3*F_38(x))
Eq(F_146(x), F_147(x)*F_4(x))
Eq(F_147(x), F_148(x) + F_149(x))
Eq(F_148(x), F_143(x))
Eq(F_149(x), F_146(x))
Eq(F_150(x), F_151(x)*F_4(x))
Eq(F_151(x), F_113(x) + F_152(x))
Eq(F_152(x), F_140(x))
Eq(F_153(x), F_154(x)*F_4(x))
Eq(F_154(x), F_155(x) + F_180(x))
Eq(F_155(x), F_156(x) + F_30(x))
Eq(F_156(x), F_157(x) + F_177(x) + F_38(x))
Eq(F_157(x), F_158(x)*F_4(x))
Eq(F_158(x), F_159(x) + F_164(x))
Eq(F_159(x), F_11(x) + F_160(x))
Eq(F_160(x), F_161(x) + F_38(x) + F_73(x))
Eq(F_161(x), F_162(x)*F_4(x))
Eq(F_162(x), F_163(x) + F_34(x))
Eq(F_163(x), F_161(x) + F_38(x) + F_43(x))
Eq(F_164(x), F_113(x) + F_165(x))
Eq(F_165(x), F_150(x) + F_166(x) + 2*F_38(x))
Eq(F_166(x), F_167(x)*F_4(x))
Eq(F_167(x), F_168(x) + F_170(x))
Eq(F_168(x), F_160(x) + F_169(x))
Eq(F_169(x), F_128(x))
Eq(F_170(x), F_171(x) + F_172(x))
Eq(F_171(x), F_166(x))
Eq(F_172(x), F_137(x) + F_173(x) + 3*F_38(x))
Eq(F_173(x), F_174(x)*F_4(x))
Eq(F_174(x), F_175(x) + F_176(x))
Eq(F_175(x), F_169(x))
Eq(F_176(x), F_173(x))
Eq(F_177(x), F_178(x)*F_4(x))
Eq(F_178(x), F_179(x) + F_30(x))
Eq(F_179(x), F_177(x) + F_38(x) + F_54(x))
Eq(F_180(x), F_181(x) + F_190(x))
Eq(F_181(x), F_182(x) + F_38(x) + F_39(x))
Eq(F_182(x), F_183(x)*F_4(x))
Eq(F_183(x), F_184(x) + F_65(x))
Eq(F_184(x), F_181(x) + F_185(x))
Eq(F_185(x), F_186(x) + 2*F_38(x) + F_60(x))
Eq(F_186(x), F_187(x)*F_4(x))
Eq(F_187(x), F_188(x) + F_52(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_186(x) + 2*F_38(x) + F_60(x))
Eq(F_190(x), F_191(x) + F_195(x) + 2*F_38(x))
Eq(F_191(x), F_192(x)*F_4(x))
Eq(F_192(x), F_193(x) + F_194(x))
Eq(F_193(x), F_81(x))
Eq(F_194(x), F_119(x))
Eq(F_195(x), F_196(x)*F_4(x))
Eq(F_196(x), F_112(x) + F_197(x))
Eq(F_197(x), F_198(x))
Eq(F_198(x), F_119(x) + F_195(x) + 2*F_38(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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 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, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 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, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 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, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 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, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], 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