0123_0231_0321_1230_2130
Counting sequence:
1, 1, 2, 6, 19, 54, 135, 318, 718, 1566, 3336, 6978, 14385, 29314, 59173, 118506, 235756, 466346, 917934, 1799054, 3512607, 6835230, 13260835, 25657542, 49522074, 95371750, 183300020, 351642282, 673442461, 1287710282, 2458697409, 4688206482, 8928198424, 16982945298, 32269133786, 61251488342, 116152404843, 220062858822, 416576632127, 787940445198, 1489228197542, 2812651965806, 5308524110304, 10012662727762, 18873707450697, 35555724891474, 66945052773597, 125978142068986, 236946364993668, 445443619752762, 837013288944774, 1572089940996702, 2951452739045623, 5538793687773358, 10390166643258843, 19483386953658646, 36521389162501106, 68434788796252854, 128191426710637964, 240048354382261818, 449367027437082165, 840951877589006746, 1573305535728174969, 2942600243681042466, 5502116805303851824, 10285195812265299746, 19221321040034830770, 35912474212246477222, 67081413025525969859, 125272878972213771606, 233890699420014569463, 436589017283168517598, 814778225445245909886, 1520251530993720605630, 2835982018202689899704, 5289394237737351941730, 9863367083355304448865, 18389228343293138685218, 34278596427900824999061, 63886022918483632453130, 119045770521124782775580, 221793750526405821109194, 413155658520292368177502, 769500577612444871421486, 1432968859916939672788431, 2668079481906373555666494, 4967027576594873254594963, 9245527834691794893127782, 17207019852482461911464778, 32019890796491273832059526, 59576590891950703027677540, 110834354441221175143174858, 206166156970967204538782413, 383447428454025044008503786, 713084439757700173897173553, 1325940172065369186485911730, 2465221013201143879938622536, 4582873244722426230116905778, 8518653169493878525925123466, 15832742759544650330706566646, 29423510865091309000653392155
Generating function in Maple syntax:
-(x^8+2*x^6+7*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{x^{8}+2 x^{6}+7 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:
(-x**8 - 2*x**6 - 7*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)+x^8+2*x^6+7*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)+x^{8}+2 x^{6}+7 x^{5}+7 x^{4}+2 x^{3}-2 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/5808*((-561*(-447/187+n)*(I+1/3*3^(1/2))*11^(1/2)+1001*(n-207/91)*(1+I*3^(1/2)))*(17+3*11^(1/2)*3^(1/2))^(1/3)+(-132*(I-1/3*3^(1/2))*(n-48/11)*11^(1/2)+374*(I*3^(1/2)-1)*(n-63/17))*(17+3*11^(1/2)*3^(1/2))^(2/3)+2992*n-8712)*(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)+1/5808*((561*(I-1/3*3^(1/2))*(-447/187+n)*11^(1/2)-1001*(I*3^(1/2)-1)*(n-207/91))*(17+3*11^(1/2)*3^(1/2))^(1/3)+(132*(n-48/11)*(I+1/3*3^(1/2))*11^(1/2)-374*(1+I*3^(1/2))*(n-63/17))*(17+3*11^(1/2)*3^(1/2))^(2/3)+2992*n-8712)*(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)+9/2+1/5808*(((374*n-894)*3^(1/2)*11^(1/2)-2002*n+4554)*(17+3*11^(1/2)*3^(1/2))^(1/3)+((-88*n+384)*3^(1/2)*11^(1/2)+748*n-2772)*(17+3*11^(1/2)*3^(1/2))^(2/3)+2992*n-8712)*(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(-561 \left(-\frac{447}{187}+n \right) \left(\mathrm{I}+\frac{\sqrt{3}}{3}\right) \sqrt{11}+1001 \left(n -\frac{207}{91}\right) \left(1+\mathrm{I} \sqrt{3}\right)\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+\left(-132 \left(\mathrm{I}-\frac{\sqrt{3}}{3}\right) \left(n -\frac{48}{11}\right) \sqrt{11}+374 \left(\mathrm{I} \sqrt{3}-1\right) \left(n -\frac{63}{17}\right)\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+2992 n -8712\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}}{5808}\\+\\\frac{\left(\left(561 \left(\mathrm{I}-\frac{\sqrt{3}}{3}\right) \left(-\frac{447}{187}+n \right) \sqrt{11}-1001 \left(\mathrm{I} \sqrt{3}-1\right) \left(n -\frac{207}{91}\right)\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+\left(132 \left(n -\frac{48}{11}\right) \left(\mathrm{I}+\frac{\sqrt{3}}{3}\right) \sqrt{11}-374 \left(1+\mathrm{I} \sqrt{3}\right) \left(n -\frac{63}{17}\right)\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+2992 n -8712\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}}{5808}\\+\frac{9}{2}+\\\frac{\left(\left(\left(374 n -894\right) \sqrt{3}\, \sqrt{11}-2002 n +4554\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+\left(\left(-88 n +384\right) \sqrt{3}\, \sqrt{11}+748 n -2772\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+2992 n -8712\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}}{5808} & \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) = 54
a(6) = 135
a(7) = 318
a(8) = 718
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)+6, 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) = 54
a \! \left(6\right) = 135
a \! \left(7\right) = 318
a \! \left(8\right) = 718
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}+6, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17106/
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[20,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[18,x] = F[19,x]*F[4,x]
F[19,x] = F[11,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[257,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[42,x]
F[25,x] = F[26,x]+F[7,x]
F[26,x] = F[22,x]+F[27,x]+F[37,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[33,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[4,x]
F[33,x] = F[17,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[30,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[14,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[4,x]
F[42,x] = F[129,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[52,x]
F[46,x] = F[47,x]+F[7,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[51,x]
F[50,x] = F[11,x]
F[51,x] = F[17,x]
F[52,x] = F[43,x]+F[53,x]
F[53,x] = 2*F[22,x]+F[54,x]+F[75,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[60,x]
F[56,x] = F[47,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[51,x]
F[60,x] = F[61,x]+F[66,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[47,x]
F[65,x] = F[61,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[57,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[57,x]
F[74,x] = F[71,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[104,x]+F[77,x]
F[77,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[83,x]
F[81,x] = F[11,x]+F[82,x]
F[82,x] = F[48,x]
F[83,x] = F[78,x]+F[84,x]
F[84,x] = 2*F[22,x]+F[75,x]+F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[87,x]+F[89,x]
F[87,x] = F[82,x]+F[88,x]
F[88,x] = F[58,x]
F[89,x] = F[90,x]+F[95,x]
F[90,x] = F[91,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[82,x]
F[94,x] = F[90,x]
F[95,x] = F[96,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[98,x]+F[99,x]
F[98,x] = F[88,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[88,x]
F[103,x] = F[100,x]
F[104,x] = F[105,x]
F[105,x] = 2*F[22,x]+F[106,x]+F[127,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[108,x]+F[112,x]
F[108,x] = F[109,x]+F[17,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[17,x]
F[112,x] = F[113,x]+F[118,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[17,x]
F[117,x] = F[113,x]
F[118,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[109,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[4,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[109,x]
F[126,x] = F[123,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[78,x]
F[129,x] = 2*F[22,x]+F[130,x]+F[253,x]
F[130,x] = F[131,x]*F[4,x]
F[131,x] = F[132,x]+F[140,x]
F[132,x] = F[133,x]+F[26,x]
F[133,x] = 2*F[22,x]+F[134,x]+F[138,x]
F[134,x] = F[135,x]*F[4,x]
F[135,x] = F[136,x]+F[137,x]
F[136,x] = F[30,x]
F[137,x] = F[34,x]
F[138,x] = F[139,x]*F[4,x]
F[139,x] = F[33,x]
F[140,x] = F[141,x]+F[227,x]
F[141,x] = F[142,x]
F[142,x] = F[143,x]*F[4,x]
F[143,x] = F[144,x]+F[150,x]
F[144,x] = F[145,x]+F[26,x]
F[145,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[30,x]
F[149,x] = F[34,x]
F[150,x] = F[141,x]+F[151,x]
F[151,x] = 3*F[22,x]+F[152,x]+F[173,x]
F[152,x] = F[153,x]*F[4,x]
F[153,x] = F[154,x]+F[158,x]
F[154,x] = F[145,x]+F[155,x]
F[155,x] = F[156,x]
F[156,x] = F[157,x]*F[4,x]
F[157,x] = F[149,x]
F[158,x] = F[159,x]+F[164,x]
F[159,x] = F[160,x]
F[160,x] = F[161,x]*F[4,x]
F[161,x] = F[162,x]+F[163,x]
F[162,x] = F[145,x]
F[163,x] = F[159,x]
F[164,x] = F[165,x]
F[165,x] = F[166,x]*F[4,x]
F[166,x] = F[167,x]+F[168,x]
F[167,x] = F[155,x]
F[168,x] = F[169,x]
F[169,x] = F[170,x]*F[4,x]
F[170,x] = F[171,x]+F[172,x]
F[171,x] = F[155,x]
F[172,x] = F[169,x]
F[173,x] = F[174,x]*F[4,x]
F[174,x] = F[175,x]+F[202,x]
F[175,x] = F[176,x]
F[176,x] = F[177,x]
F[177,x] = F[178,x]*F[4,x]
F[178,x] = F[179,x]+F[181,x]
F[179,x] = F[180,x]+F[30,x]
F[180,x] = F[146,x]
F[181,x] = F[176,x]+F[182,x]
F[182,x] = 3*F[22,x]+F[173,x]+F[183,x]
F[183,x] = F[184,x]*F[4,x]
F[184,x] = F[185,x]+F[187,x]
F[185,x] = F[180,x]+F[186,x]
F[186,x] = F[156,x]
F[187,x] = F[188,x]+F[193,x]
F[188,x] = F[189,x]
F[189,x] = F[190,x]*F[4,x]
F[190,x] = F[191,x]+F[192,x]
F[191,x] = F[180,x]
F[192,x] = F[188,x]
F[193,x] = F[194,x]
F[194,x] = F[195,x]*F[4,x]
F[195,x] = F[196,x]+F[197,x]
F[196,x] = F[186,x]
F[197,x] = F[198,x]
F[198,x] = F[199,x]*F[4,x]
F[199,x] = F[200,x]+F[201,x]
F[200,x] = F[186,x]
F[201,x] = F[198,x]
F[202,x] = F[203,x]
F[203,x] = 3*F[22,x]+F[204,x]+F[225,x]
F[204,x] = F[205,x]*F[4,x]
F[205,x] = F[206,x]+F[210,x]
F[206,x] = F[207,x]+F[34,x]
F[207,x] = F[208,x]
F[208,x] = F[209,x]*F[4,x]
F[209,x] = F[34,x]
F[210,x] = F[211,x]+F[216,x]
F[211,x] = F[212,x]
F[212,x] = F[213,x]*F[4,x]
F[213,x] = F[214,x]+F[215,x]
F[214,x] = F[34,x]
F[215,x] = F[211,x]
F[216,x] = F[217,x]
F[217,x] = F[218,x]*F[4,x]
F[218,x] = F[219,x]+F[220,x]
F[219,x] = F[207,x]
F[220,x] = F[221,x]
F[221,x] = F[222,x]*F[4,x]
F[222,x] = F[223,x]+F[224,x]
F[223,x] = F[207,x]
F[224,x] = F[221,x]
F[225,x] = F[226,x]*F[4,x]
F[226,x] = F[176,x]
F[227,x] = 3*F[22,x]+F[228,x]+F[249,x]
F[228,x] = F[229,x]*F[4,x]
F[229,x] = F[230,x]+F[234,x]
F[230,x] = F[133,x]+F[231,x]
F[231,x] = F[232,x]
F[232,x] = F[233,x]*F[4,x]
F[233,x] = F[137,x]
F[234,x] = F[235,x]+F[240,x]
F[235,x] = F[236,x]
F[236,x] = F[237,x]*F[4,x]
F[237,x] = F[238,x]+F[239,x]
F[238,x] = F[133,x]
F[239,x] = F[235,x]
F[240,x] = F[241,x]
F[241,x] = F[242,x]*F[4,x]
F[242,x] = F[243,x]+F[244,x]
F[243,x] = F[231,x]
F[244,x] = F[245,x]
F[245,x] = F[246,x]*F[4,x]
F[246,x] = F[247,x]+F[248,x]
F[247,x] = F[231,x]
F[248,x] = F[245,x]
F[249,x] = F[250,x]*F[4,x]
F[250,x] = F[251,x]+F[252,x]
F[251,x] = F[176,x]
F[252,x] = F[203,x]
F[253,x] = F[254,x]*F[4,x]
F[254,x] = F[255,x]+F[256,x]
F[255,x] = F[176,x]+F[78,x]
F[256,x] = F[105,x]+F[203,x]
F[257,x] = F[258,x]*F[4,x]
F[258,x] = F[259,x]+F[260,x]
F[259,x] = F[2,x]+F[78,x]
F[260,x] = F[105,x]+F[261,x]
F[261,x] = F[22,x]+F[262,x]+F[493,x]
F[262,x] = F[263,x]*F[4,x]
F[263,x] = F[264,x]+F[278,x]
F[264,x] = F[15,x]+F[265,x]
F[265,x] = F[22,x]+F[266,x]+F[276,x]
F[266,x] = F[267,x]*F[4,x]
F[267,x] = F[268,x]+F[271,x]
F[268,x] = F[269,x]+F[4,x]
F[269,x] = F[270,x]
F[270,x] = x^2
F[271,x] = F[272,x]+F[273,x]
F[272,x] = F[40,x]
F[273,x] = F[274,x]
F[274,x] = F[275,x]*F[4,x]
F[275,x] = F[269,x]
F[276,x] = F[277,x]*F[4,x]
F[277,x] = F[15,x]+F[272,x]
F[278,x] = F[279,x]+F[365,x]
F[279,x] = F[280,x]
F[280,x] = F[281,x]*F[4,x]
F[281,x] = F[282,x]+F[288,x]
F[282,x] = F[15,x]+F[283,x]
F[283,x] = F[284,x]
F[284,x] = F[285,x]*F[4,x]
F[285,x] = F[286,x]+F[287,x]
F[286,x] = F[4,x]
F[287,x] = F[272,x]
F[288,x] = F[279,x]+F[289,x]
F[289,x] = 2*F[22,x]+F[290,x]+F[311,x]
F[290,x] = F[291,x]*F[4,x]
F[291,x] = F[292,x]+F[296,x]
F[292,x] = F[283,x]+F[293,x]
F[293,x] = F[294,x]
F[294,x] = F[295,x]*F[4,x]
F[295,x] = F[287,x]
F[296,x] = F[297,x]+F[302,x]
F[297,x] = F[298,x]
F[298,x] = F[299,x]*F[4,x]
F[299,x] = F[300,x]+F[301,x]
F[300,x] = F[283,x]
F[301,x] = F[297,x]
F[302,x] = F[303,x]
F[303,x] = F[304,x]*F[4,x]
F[304,x] = F[305,x]+F[306,x]
F[305,x] = F[293,x]
F[306,x] = F[307,x]
F[307,x] = F[308,x]*F[4,x]
F[308,x] = F[309,x]+F[310,x]
F[309,x] = F[293,x]
F[310,x] = F[307,x]
F[311,x] = F[312,x]*F[4,x]
F[312,x] = F[313,x]+F[340,x]
F[313,x] = F[314,x]
F[314,x] = F[315,x]
F[315,x] = F[316,x]*F[4,x]
F[316,x] = F[317,x]+F[319,x]
F[317,x] = F[318,x]+F[4,x]
F[318,x] = F[284,x]
F[319,x] = F[314,x]+F[320,x]
F[320,x] = 2*F[22,x]+F[311,x]+F[321,x]
F[321,x] = F[322,x]*F[4,x]
F[322,x] = F[323,x]+F[325,x]
F[323,x] = F[318,x]+F[324,x]
F[324,x] = F[294,x]
F[325,x] = F[326,x]+F[331,x]
F[326,x] = F[327,x]
F[327,x] = F[328,x]*F[4,x]
F[328,x] = F[329,x]+F[330,x]
F[329,x] = F[318,x]
F[330,x] = F[326,x]
F[331,x] = F[332,x]
F[332,x] = F[333,x]*F[4,x]
F[333,x] = F[334,x]+F[335,x]
F[334,x] = F[324,x]
F[335,x] = F[336,x]
F[336,x] = F[337,x]*F[4,x]
F[337,x] = F[338,x]+F[339,x]
F[338,x] = F[324,x]
F[339,x] = F[336,x]
F[340,x] = F[341,x]
F[341,x] = 2*F[22,x]+F[342,x]+F[363,x]
F[342,x] = F[343,x]*F[4,x]
F[343,x] = F[344,x]+F[348,x]
F[344,x] = F[272,x]+F[345,x]
F[345,x] = F[346,x]
F[346,x] = F[347,x]*F[4,x]
F[347,x] = F[272,x]
F[348,x] = F[349,x]+F[354,x]
F[349,x] = F[350,x]
F[350,x] = F[351,x]*F[4,x]
F[351,x] = F[352,x]+F[353,x]
F[352,x] = F[272,x]
F[353,x] = F[349,x]
F[354,x] = F[355,x]
F[355,x] = F[356,x]*F[4,x]
F[356,x] = F[357,x]+F[358,x]
F[357,x] = F[345,x]
F[358,x] = F[359,x]
F[359,x] = F[360,x]*F[4,x]
F[360,x] = F[361,x]+F[362,x]
F[361,x] = F[345,x]
F[362,x] = F[359,x]
F[363,x] = F[364,x]*F[4,x]
F[364,x] = F[314,x]
F[365,x] = 2*F[22,x]+F[366,x]+F[489,x]
F[366,x] = F[367,x]*F[4,x]
F[367,x] = F[368,x]+F[376,x]
F[368,x] = F[265,x]+F[369,x]
F[369,x] = 2*F[22,x]+F[370,x]+F[374,x]
F[370,x] = F[371,x]*F[4,x]
F[371,x] = F[372,x]+F[373,x]
F[372,x] = F[269,x]
F[373,x] = F[273,x]
F[374,x] = F[375,x]*F[4,x]
F[375,x] = F[271,x]
F[376,x] = F[377,x]+F[463,x]
F[377,x] = F[378,x]
F[378,x] = F[379,x]*F[4,x]
F[379,x] = F[380,x]+F[386,x]
F[380,x] = F[265,x]+F[381,x]
F[381,x] = F[382,x]
F[382,x] = F[383,x]*F[4,x]
F[383,x] = F[384,x]+F[385,x]
F[384,x] = F[269,x]
F[385,x] = F[273,x]
F[386,x] = F[377,x]+F[387,x]
F[387,x] = 3*F[22,x]+F[388,x]+F[409,x]
F[388,x] = F[389,x]*F[4,x]
F[389,x] = F[390,x]+F[394,x]
F[390,x] = F[381,x]+F[391,x]
F[391,x] = F[392,x]
F[392,x] = F[393,x]*F[4,x]
F[393,x] = F[385,x]
F[394,x] = F[395,x]+F[400,x]
F[395,x] = F[396,x]
F[396,x] = F[397,x]*F[4,x]
F[397,x] = F[398,x]+F[399,x]
F[398,x] = F[381,x]
F[399,x] = F[395,x]
F[400,x] = F[401,x]
F[401,x] = F[4,x]*F[402,x]
F[402,x] = F[403,x]+F[404,x]
F[403,x] = F[391,x]
F[404,x] = F[405,x]
F[405,x] = F[4,x]*F[406,x]
F[406,x] = F[407,x]+F[408,x]
F[407,x] = F[391,x]
F[408,x] = F[405,x]
F[409,x] = F[4,x]*F[410,x]
F[410,x] = F[411,x]+F[438,x]
F[411,x] = F[412,x]
F[412,x] = F[413,x]
F[413,x] = F[4,x]*F[414,x]
F[414,x] = F[415,x]+F[417,x]
F[415,x] = F[269,x]+F[416,x]
F[416,x] = F[382,x]
F[417,x] = F[412,x]+F[418,x]
F[418,x] = 3*F[22,x]+F[409,x]+F[419,x]
F[419,x] = F[4,x]*F[420,x]
F[420,x] = F[421,x]+F[423,x]
F[421,x] = F[416,x]+F[422,x]
F[422,x] = F[392,x]
F[423,x] = F[424,x]+F[429,x]
F[424,x] = F[425,x]
F[425,x] = F[4,x]*F[426,x]
F[426,x] = F[427,x]+F[428,x]
F[427,x] = F[416,x]
F[428,x] = F[424,x]
F[429,x] = F[430,x]
F[430,x] = F[4,x]*F[431,x]
F[431,x] = F[432,x]+F[433,x]
F[432,x] = F[422,x]
F[433,x] = F[434,x]
F[434,x] = F[4,x]*F[435,x]
F[435,x] = F[436,x]+F[437,x]
F[436,x] = F[422,x]
F[437,x] = F[434,x]
F[438,x] = F[439,x]
F[439,x] = 3*F[22,x]+F[440,x]+F[461,x]
F[440,x] = F[4,x]*F[441,x]
F[441,x] = F[442,x]+F[446,x]
F[442,x] = F[273,x]+F[443,x]
F[443,x] = F[444,x]
F[444,x] = F[4,x]*F[445,x]
F[445,x] = F[273,x]
F[446,x] = F[447,x]+F[452,x]
F[447,x] = F[448,x]
F[448,x] = F[4,x]*F[449,x]
F[449,x] = F[450,x]+F[451,x]
F[450,x] = F[273,x]
F[451,x] = F[447,x]
F[452,x] = F[453,x]
F[453,x] = F[4,x]*F[454,x]
F[454,x] = F[455,x]+F[456,x]
F[455,x] = F[443,x]
F[456,x] = F[457,x]
F[457,x] = F[4,x]*F[458,x]
F[458,x] = F[459,x]+F[460,x]
F[459,x] = F[443,x]
F[460,x] = F[457,x]
F[461,x] = F[4,x]*F[462,x]
F[462,x] = F[412,x]
F[463,x] = 3*F[22,x]+F[464,x]+F[485,x]
F[464,x] = F[4,x]*F[465,x]
F[465,x] = F[466,x]+F[470,x]
F[466,x] = F[369,x]+F[467,x]
F[467,x] = F[468,x]
F[468,x] = F[4,x]*F[469,x]
F[469,x] = F[373,x]
F[470,x] = F[471,x]+F[476,x]
F[471,x] = F[472,x]
F[472,x] = F[4,x]*F[473,x]
F[473,x] = F[474,x]+F[475,x]
F[474,x] = F[369,x]
F[475,x] = F[471,x]
F[476,x] = F[477,x]
F[477,x] = F[4,x]*F[478,x]
F[478,x] = F[479,x]+F[480,x]
F[479,x] = F[467,x]
F[480,x] = F[481,x]
F[481,x] = F[4,x]*F[482,x]
F[482,x] = F[483,x]+F[484,x]
F[483,x] = F[467,x]
F[484,x] = F[481,x]
F[485,x] = F[4,x]*F[486,x]
F[486,x] = F[487,x]+F[488,x]
F[487,x] = F[412,x]
F[488,x] = F[439,x]
F[489,x] = F[4,x]*F[490,x]
F[490,x] = F[491,x]+F[492,x]
F[491,x] = F[314,x]+F[412,x]
F[492,x] = F[341,x]+F[439,x]
F[493,x] = F[4,x]*F[494,x]
F[494,x] = F[2,x]+F[314,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_{20}\! \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_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{257}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{42}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{7}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{37}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{30}\! \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_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{17}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{129}\! \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_{52}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{7}\! \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_{51}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right)
F_{51}\! \left(x \right) = F_{17}\! \left(x \right)
F_{52}\! \left(x \right) = F_{43}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{54}\! \left(x \right)+F_{75}\! \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_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{47}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{51}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{66}\! \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_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{47}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{57}\! \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_{57}\! \left(x \right)
F_{74}\! \left(x \right) = F_{71}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{104}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \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_{83}\! \left(x \right)
F_{81}\! \left(x \right) = F_{11}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{48}\! \left(x \right)
F_{83}\! \left(x \right) = F_{78}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{75}\! \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_{89}\! \left(x \right)
F_{87}\! \left(x \right) = F_{82}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{58}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{95}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{82}\! \left(x \right)
F_{94}\! \left(x \right) = F_{90}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)+F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{88}\! \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_{88}\! \left(x \right)
F_{103}\! \left(x \right) = F_{100}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{106}\! \left(x \right)+F_{127}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{112}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{17}\! \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_{17}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{118}\! \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_{17}\! \left(x \right)
F_{117}\! \left(x \right) = F_{113}\! \left(x \right)
F_{118}\! \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_{109}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{4}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{126}\! \left(x \right)
F_{125}\! \left(x \right) = F_{109}\! \left(x \right)
F_{126}\! \left(x \right) = F_{123}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = F_{78}\! \left(x \right)
F_{129}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{130}\! \left(x \right)+F_{253}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{4}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{140}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{26}\! \left(x \right)
F_{133}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{134}\! \left(x \right)+F_{138}\! \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_{137}\! \left(x \right)
F_{136}\! \left(x \right) = F_{30}\! \left(x \right)
F_{137}\! \left(x \right) = F_{34}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{4}\! \left(x \right)
F_{139}\! \left(x \right) = F_{33}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{227}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \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_{150}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{26}\! \left(x \right)
F_{145}\! \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_{30}\! \left(x \right)
F_{149}\! \left(x \right) = F_{34}\! \left(x \right)
F_{150}\! \left(x \right) = F_{141}\! \left(x \right)+F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{152}\! \left(x \right)+F_{173}\! \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_{158}\! \left(x \right)
F_{154}\! \left(x \right) = F_{145}\! \left(x \right)+F_{155}\! \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_{149}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{164}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \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_{163}\! \left(x \right)
F_{162}\! \left(x \right) = F_{145}\! \left(x \right)
F_{163}\! \left(x \right) = F_{159}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{4}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{168}\! \left(x \right)
F_{167}\! \left(x \right) = F_{155}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right) F_{4}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)+F_{172}\! \left(x \right)
F_{171}\! \left(x \right) = F_{155}\! \left(x \right)
F_{172}\! \left(x \right) = F_{169}\! \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_{202}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \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_{181}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{30}\! \left(x \right)
F_{180}\! \left(x \right) = F_{146}\! \left(x \right)
F_{181}\! \left(x \right) = F_{176}\! \left(x \right)+F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{173}\! \left(x \right)+F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right) F_{4}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{187}\! \left(x \right)
F_{185}\! \left(x \right) = F_{180}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{156}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{193}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right) F_{4}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{192}\! \left(x \right)
F_{191}\! \left(x \right) = F_{180}\! \left(x \right)
F_{192}\! \left(x \right) = F_{188}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right) F_{4}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)+F_{197}\! \left(x \right)
F_{196}\! \left(x \right) = F_{186}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right) F_{4}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)+F_{201}\! \left(x \right)
F_{200}\! \left(x \right) = F_{186}\! \left(x \right)
F_{201}\! \left(x \right) = F_{198}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{204}\! \left(x \right)+F_{225}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right) F_{4}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)+F_{210}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)+F_{34}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right) F_{4}\! \left(x \right)
F_{209}\! \left(x \right) = F_{34}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{216}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right) F_{4}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right)+F_{215}\! \left(x \right)
F_{214}\! \left(x \right) = F_{34}\! \left(x \right)
F_{215}\! \left(x \right) = F_{211}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right) F_{4}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right)+F_{220}\! \left(x \right)
F_{219}\! \left(x \right) = F_{207}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right) F_{4}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)+F_{224}\! \left(x \right)
F_{223}\! \left(x \right) = F_{207}\! \left(x \right)
F_{224}\! \left(x \right) = F_{221}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right) F_{4}\! \left(x \right)
F_{226}\! \left(x \right) = F_{176}\! \left(x \right)
F_{227}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{228}\! \left(x \right)+F_{249}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right) F_{4}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)+F_{234}\! \left(x \right)
F_{230}\! \left(x \right) = F_{133}\! \left(x \right)+F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right) F_{4}\! \left(x \right)
F_{233}\! \left(x \right) = F_{137}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)+F_{240}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right) F_{4}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)+F_{239}\! \left(x \right)
F_{238}\! \left(x \right) = F_{133}\! \left(x \right)
F_{239}\! \left(x \right) = F_{235}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right) F_{4}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)+F_{244}\! \left(x \right)
F_{243}\! \left(x \right) = F_{231}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x \right) F_{4}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right)+F_{248}\! \left(x \right)
F_{247}\! \left(x \right) = F_{231}\! \left(x \right)
F_{248}\! \left(x \right) = F_{245}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right) F_{4}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right)+F_{252}\! \left(x \right)
F_{251}\! \left(x \right) = F_{176}\! \left(x \right)
F_{252}\! \left(x \right) = F_{203}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right) F_{4}\! \left(x \right)
F_{254}\! \left(x \right) = F_{255}\! \left(x \right)+F_{256}\! \left(x \right)
F_{255}\! \left(x \right) = F_{176}\! \left(x \right)+F_{78}\! \left(x \right)
F_{256}\! \left(x \right) = F_{105}\! \left(x \right)+F_{203}\! \left(x \right)
F_{257}\! \left(x \right) = F_{258}\! \left(x \right) F_{4}\! \left(x \right)
F_{258}\! \left(x \right) = F_{259}\! \left(x \right)+F_{260}\! \left(x \right)
F_{259}\! \left(x \right) = F_{2}\! \left(x \right)+F_{78}\! \left(x \right)
F_{260}\! \left(x \right) = F_{105}\! \left(x \right)+F_{261}\! \left(x \right)
F_{261}\! \left(x \right) = F_{22}\! \left(x \right)+F_{262}\! \left(x \right)+F_{493}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right) F_{4}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right)+F_{278}\! \left(x \right)
F_{264}\! \left(x \right) = F_{15}\! \left(x \right)+F_{265}\! \left(x \right)
F_{265}\! \left(x \right) = F_{22}\! \left(x \right)+F_{266}\! \left(x \right)+F_{276}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right) F_{4}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)+F_{271}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right)+F_{4}\! \left(x \right)
F_{269}\! \left(x \right) = F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = x^{2}
F_{271}\! \left(x \right) = F_{272}\! \left(x \right)+F_{273}\! \left(x \right)
F_{272}\! \left(x \right) = F_{40}\! \left(x \right)
F_{273}\! \left(x \right) = F_{274}\! \left(x \right)
F_{274}\! \left(x \right) = F_{275}\! \left(x \right) F_{4}\! \left(x \right)
F_{275}\! \left(x \right) = F_{269}\! \left(x \right)
F_{276}\! \left(x \right) = F_{277}\! \left(x \right) F_{4}\! \left(x \right)
F_{277}\! \left(x \right) = F_{15}\! \left(x \right)+F_{272}\! \left(x \right)
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)+F_{365}\! \left(x \right)
F_{279}\! \left(x \right) = F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = F_{281}\! \left(x \right) F_{4}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x \right)+F_{288}\! \left(x \right)
F_{282}\! \left(x \right) = F_{15}\! \left(x \right)+F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = F_{285}\! \left(x \right) F_{4}\! \left(x \right)
F_{285}\! \left(x \right) = F_{286}\! \left(x \right)+F_{287}\! \left(x \right)
F_{286}\! \left(x \right) = F_{4}\! \left(x \right)
F_{287}\! \left(x \right) = F_{272}\! \left(x \right)
F_{288}\! \left(x \right) = F_{279}\! \left(x \right)+F_{289}\! \left(x \right)
F_{289}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{290}\! \left(x \right)+F_{311}\! \left(x \right)
F_{290}\! \left(x \right) = F_{291}\! \left(x \right) F_{4}\! \left(x \right)
F_{291}\! \left(x \right) = F_{292}\! \left(x \right)+F_{296}\! \left(x \right)
F_{292}\! \left(x \right) = F_{283}\! \left(x \right)+F_{293}\! \left(x \right)
F_{293}\! \left(x \right) = F_{294}\! \left(x \right)
F_{294}\! \left(x \right) = F_{295}\! \left(x \right) F_{4}\! \left(x \right)
F_{295}\! \left(x \right) = F_{287}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right)+F_{302}\! \left(x \right)
F_{297}\! \left(x \right) = F_{298}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right) F_{4}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)+F_{301}\! \left(x \right)
F_{300}\! \left(x \right) = F_{283}\! \left(x \right)
F_{301}\! \left(x \right) = F_{297}\! \left(x \right)
F_{302}\! \left(x \right) = F_{303}\! \left(x \right)
F_{303}\! \left(x \right) = F_{304}\! \left(x \right) F_{4}\! \left(x \right)
F_{304}\! \left(x \right) = F_{305}\! \left(x \right)+F_{306}\! \left(x \right)
F_{305}\! \left(x \right) = F_{293}\! \left(x \right)
F_{306}\! \left(x \right) = F_{307}\! \left(x \right)
F_{307}\! \left(x \right) = F_{308}\! \left(x \right) F_{4}\! \left(x \right)
F_{308}\! \left(x \right) = F_{309}\! \left(x \right)+F_{310}\! \left(x \right)
F_{309}\! \left(x \right) = F_{293}\! \left(x \right)
F_{310}\! \left(x \right) = F_{307}\! \left(x \right)
F_{311}\! \left(x \right) = F_{312}\! \left(x \right) F_{4}\! \left(x \right)
F_{312}\! \left(x \right) = F_{313}\! \left(x \right)+F_{340}\! \left(x \right)
F_{313}\! \left(x \right) = F_{314}\! \left(x \right)
F_{314}\! \left(x \right) = F_{315}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right) F_{4}\! \left(x \right)
F_{316}\! \left(x \right) = F_{317}\! \left(x \right)+F_{319}\! \left(x \right)
F_{317}\! \left(x \right) = F_{318}\! \left(x \right)+F_{4}\! \left(x \right)
F_{318}\! \left(x \right) = F_{284}\! \left(x \right)
F_{319}\! \left(x \right) = F_{314}\! \left(x \right)+F_{320}\! \left(x \right)
F_{320}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{311}\! \left(x \right)+F_{321}\! \left(x \right)
F_{321}\! \left(x \right) = F_{322}\! \left(x \right) F_{4}\! \left(x \right)
F_{322}\! \left(x \right) = F_{323}\! \left(x \right)+F_{325}\! \left(x \right)
F_{323}\! \left(x \right) = F_{318}\! \left(x \right)+F_{324}\! \left(x \right)
F_{324}\! \left(x \right) = F_{294}\! \left(x \right)
F_{325}\! \left(x \right) = F_{326}\! \left(x \right)+F_{331}\! \left(x \right)
F_{326}\! \left(x \right) = F_{327}\! \left(x \right)
F_{327}\! \left(x \right) = F_{328}\! \left(x \right) F_{4}\! \left(x \right)
F_{328}\! \left(x \right) = F_{329}\! \left(x \right)+F_{330}\! \left(x \right)
F_{329}\! \left(x \right) = F_{318}\! \left(x \right)
F_{330}\! \left(x \right) = F_{326}\! \left(x \right)
F_{331}\! \left(x \right) = F_{332}\! \left(x \right)
F_{332}\! \left(x \right) = F_{333}\! \left(x \right) F_{4}\! \left(x \right)
F_{333}\! \left(x \right) = F_{334}\! \left(x \right)+F_{335}\! \left(x \right)
F_{334}\! \left(x \right) = F_{324}\! \left(x \right)
F_{335}\! \left(x \right) = F_{336}\! \left(x \right)
F_{336}\! \left(x \right) = F_{337}\! \left(x \right) F_{4}\! \left(x \right)
F_{337}\! \left(x \right) = F_{338}\! \left(x \right)+F_{339}\! \left(x \right)
F_{338}\! \left(x \right) = F_{324}\! \left(x \right)
F_{339}\! \left(x \right) = F_{336}\! \left(x \right)
F_{340}\! \left(x \right) = F_{341}\! \left(x \right)
F_{341}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{342}\! \left(x \right)+F_{363}\! \left(x \right)
F_{342}\! \left(x \right) = F_{343}\! \left(x \right) F_{4}\! \left(x \right)
F_{343}\! \left(x \right) = F_{344}\! \left(x \right)+F_{348}\! \left(x \right)
F_{344}\! \left(x \right) = F_{272}\! \left(x \right)+F_{345}\! \left(x \right)
F_{345}\! \left(x \right) = F_{346}\! \left(x \right)
F_{346}\! \left(x \right) = F_{347}\! \left(x \right) F_{4}\! \left(x \right)
F_{347}\! \left(x \right) = F_{272}\! \left(x \right)
F_{348}\! \left(x \right) = F_{349}\! \left(x \right)+F_{354}\! \left(x \right)
F_{349}\! \left(x \right) = F_{350}\! \left(x \right)
F_{350}\! \left(x \right) = F_{351}\! \left(x \right) F_{4}\! \left(x \right)
F_{351}\! \left(x \right) = F_{352}\! \left(x \right)+F_{353}\! \left(x \right)
F_{352}\! \left(x \right) = F_{272}\! \left(x \right)
F_{353}\! \left(x \right) = F_{349}\! \left(x \right)
F_{354}\! \left(x \right) = F_{355}\! \left(x \right)
F_{355}\! \left(x \right) = F_{356}\! \left(x \right) F_{4}\! \left(x \right)
F_{356}\! \left(x \right) = F_{357}\! \left(x \right)+F_{358}\! \left(x \right)
F_{357}\! \left(x \right) = F_{345}\! \left(x \right)
F_{358}\! \left(x \right) = F_{359}\! \left(x \right)
F_{359}\! \left(x \right) = F_{360}\! \left(x \right) F_{4}\! \left(x \right)
F_{360}\! \left(x \right) = F_{361}\! \left(x \right)+F_{362}\! \left(x \right)
F_{361}\! \left(x \right) = F_{345}\! \left(x \right)
F_{362}\! \left(x \right) = F_{359}\! \left(x \right)
F_{363}\! \left(x \right) = F_{364}\! \left(x \right) F_{4}\! \left(x \right)
F_{364}\! \left(x \right) = F_{314}\! \left(x \right)
F_{365}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{366}\! \left(x \right)+F_{489}\! \left(x \right)
F_{366}\! \left(x \right) = F_{367}\! \left(x \right) F_{4}\! \left(x \right)
F_{367}\! \left(x \right) = F_{368}\! \left(x \right)+F_{376}\! \left(x \right)
F_{368}\! \left(x \right) = F_{265}\! \left(x \right)+F_{369}\! \left(x \right)
F_{369}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{370}\! \left(x \right)+F_{374}\! \left(x \right)
F_{370}\! \left(x \right) = F_{371}\! \left(x \right) F_{4}\! \left(x \right)
F_{371}\! \left(x \right) = F_{372}\! \left(x \right)+F_{373}\! \left(x \right)
F_{372}\! \left(x \right) = F_{269}\! \left(x \right)
F_{373}\! \left(x \right) = F_{273}\! \left(x \right)
F_{374}\! \left(x \right) = F_{375}\! \left(x \right) F_{4}\! \left(x \right)
F_{375}\! \left(x \right) = F_{271}\! \left(x \right)
F_{376}\! \left(x \right) = F_{377}\! \left(x \right)+F_{463}\! \left(x \right)
F_{377}\! \left(x \right) = F_{378}\! \left(x \right)
F_{378}\! \left(x \right) = F_{379}\! \left(x \right) F_{4}\! \left(x \right)
F_{379}\! \left(x \right) = F_{380}\! \left(x \right)+F_{386}\! \left(x \right)
F_{380}\! \left(x \right) = F_{265}\! \left(x \right)+F_{381}\! \left(x \right)
F_{381}\! \left(x \right) = F_{382}\! \left(x \right)
F_{382}\! \left(x \right) = F_{383}\! \left(x \right) F_{4}\! \left(x \right)
F_{383}\! \left(x \right) = F_{384}\! \left(x \right)+F_{385}\! \left(x \right)
F_{384}\! \left(x \right) = F_{269}\! \left(x \right)
F_{385}\! \left(x \right) = F_{273}\! \left(x \right)
F_{386}\! \left(x \right) = F_{377}\! \left(x \right)+F_{387}\! \left(x \right)
F_{387}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{388}\! \left(x \right)+F_{409}\! \left(x \right)
F_{388}\! \left(x \right) = F_{389}\! \left(x \right) F_{4}\! \left(x \right)
F_{389}\! \left(x \right) = F_{390}\! \left(x \right)+F_{394}\! \left(x \right)
F_{390}\! \left(x \right) = F_{381}\! \left(x \right)+F_{391}\! \left(x \right)
F_{391}\! \left(x \right) = F_{392}\! \left(x \right)
F_{392}\! \left(x \right) = F_{393}\! \left(x \right) F_{4}\! \left(x \right)
F_{393}\! \left(x \right) = F_{385}\! \left(x \right)
F_{394}\! \left(x \right) = F_{395}\! \left(x \right)+F_{400}\! \left(x \right)
F_{395}\! \left(x \right) = F_{396}\! \left(x \right)
F_{396}\! \left(x \right) = F_{397}\! \left(x \right) F_{4}\! \left(x \right)
F_{397}\! \left(x \right) = F_{398}\! \left(x \right)+F_{399}\! \left(x \right)
F_{398}\! \left(x \right) = F_{381}\! \left(x \right)
F_{399}\! \left(x \right) = F_{395}\! \left(x \right)
F_{400}\! \left(x \right) = F_{401}\! \left(x \right)
F_{401}\! \left(x \right) = F_{4}\! \left(x \right) F_{402}\! \left(x \right)
F_{402}\! \left(x \right) = F_{403}\! \left(x \right)+F_{404}\! \left(x \right)
F_{403}\! \left(x \right) = F_{391}\! \left(x \right)
F_{404}\! \left(x \right) = F_{405}\! \left(x \right)
F_{405}\! \left(x \right) = F_{4}\! \left(x \right) F_{406}\! \left(x \right)
F_{406}\! \left(x \right) = F_{407}\! \left(x \right)+F_{408}\! \left(x \right)
F_{407}\! \left(x \right) = F_{391}\! \left(x \right)
F_{408}\! \left(x \right) = F_{405}\! \left(x \right)
F_{409}\! \left(x \right) = F_{4}\! \left(x \right) F_{410}\! \left(x \right)
F_{410}\! \left(x \right) = F_{411}\! \left(x \right)+F_{438}\! \left(x \right)
F_{411}\! \left(x \right) = F_{412}\! \left(x \right)
F_{412}\! \left(x \right) = F_{413}\! \left(x \right)
F_{413}\! \left(x \right) = F_{4}\! \left(x \right) F_{414}\! \left(x \right)
F_{414}\! \left(x \right) = F_{415}\! \left(x \right)+F_{417}\! \left(x \right)
F_{415}\! \left(x \right) = F_{269}\! \left(x \right)+F_{416}\! \left(x \right)
F_{416}\! \left(x \right) = F_{382}\! \left(x \right)
F_{417}\! \left(x \right) = F_{412}\! \left(x \right)+F_{418}\! \left(x \right)
F_{418}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{409}\! \left(x \right)+F_{419}\! \left(x \right)
F_{419}\! \left(x \right) = F_{4}\! \left(x \right) F_{420}\! \left(x \right)
F_{420}\! \left(x \right) = F_{421}\! \left(x \right)+F_{423}\! \left(x \right)
F_{421}\! \left(x \right) = F_{416}\! \left(x \right)+F_{422}\! \left(x \right)
F_{422}\! \left(x \right) = F_{392}\! \left(x \right)
F_{423}\! \left(x \right) = F_{424}\! \left(x \right)+F_{429}\! \left(x \right)
F_{424}\! \left(x \right) = F_{425}\! \left(x \right)
F_{425}\! \left(x \right) = F_{4}\! \left(x \right) F_{426}\! \left(x \right)
F_{426}\! \left(x \right) = F_{427}\! \left(x \right)+F_{428}\! \left(x \right)
F_{427}\! \left(x \right) = F_{416}\! \left(x \right)
F_{428}\! \left(x \right) = F_{424}\! \left(x \right)
F_{429}\! \left(x \right) = F_{430}\! \left(x \right)
F_{430}\! \left(x \right) = F_{4}\! \left(x \right) F_{431}\! \left(x \right)
F_{431}\! \left(x \right) = F_{432}\! \left(x \right)+F_{433}\! \left(x \right)
F_{432}\! \left(x \right) = F_{422}\! \left(x \right)
F_{433}\! \left(x \right) = F_{434}\! \left(x \right)
F_{434}\! \left(x \right) = F_{4}\! \left(x \right) F_{435}\! \left(x \right)
F_{435}\! \left(x \right) = F_{436}\! \left(x \right)+F_{437}\! \left(x \right)
F_{436}\! \left(x \right) = F_{422}\! \left(x \right)
F_{437}\! \left(x \right) = F_{434}\! \left(x \right)
F_{438}\! \left(x \right) = F_{439}\! \left(x \right)
F_{439}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{440}\! \left(x \right)+F_{461}\! \left(x \right)
F_{440}\! \left(x \right) = F_{4}\! \left(x \right) F_{441}\! \left(x \right)
F_{441}\! \left(x \right) = F_{442}\! \left(x \right)+F_{446}\! \left(x \right)
F_{442}\! \left(x \right) = F_{273}\! \left(x \right)+F_{443}\! \left(x \right)
F_{443}\! \left(x \right) = F_{444}\! \left(x \right)
F_{444}\! \left(x \right) = F_{4}\! \left(x \right) F_{445}\! \left(x \right)
F_{445}\! \left(x \right) = F_{273}\! \left(x \right)
F_{446}\! \left(x \right) = F_{447}\! \left(x \right)+F_{452}\! \left(x \right)
F_{447}\! \left(x \right) = F_{448}\! \left(x \right)
F_{448}\! \left(x \right) = F_{4}\! \left(x \right) F_{449}\! \left(x \right)
F_{449}\! \left(x \right) = F_{450}\! \left(x \right)+F_{451}\! \left(x \right)
F_{450}\! \left(x \right) = F_{273}\! \left(x \right)
F_{451}\! \left(x \right) = F_{447}\! \left(x \right)
F_{452}\! \left(x \right) = F_{453}\! \left(x \right)
F_{453}\! \left(x \right) = F_{4}\! \left(x \right) F_{454}\! \left(x \right)
F_{454}\! \left(x \right) = F_{455}\! \left(x \right)+F_{456}\! \left(x \right)
F_{455}\! \left(x \right) = F_{443}\! \left(x \right)
F_{456}\! \left(x \right) = F_{457}\! \left(x \right)
F_{457}\! \left(x \right) = F_{4}\! \left(x \right) F_{458}\! \left(x \right)
F_{458}\! \left(x \right) = F_{459}\! \left(x \right)+F_{460}\! \left(x \right)
F_{459}\! \left(x \right) = F_{443}\! \left(x \right)
F_{460}\! \left(x \right) = F_{457}\! \left(x \right)
F_{461}\! \left(x \right) = F_{4}\! \left(x \right) F_{462}\! \left(x \right)
F_{462}\! \left(x \right) = F_{412}\! \left(x \right)
F_{463}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{464}\! \left(x \right)+F_{485}\! \left(x \right)
F_{464}\! \left(x \right) = F_{4}\! \left(x \right) F_{465}\! \left(x \right)
F_{465}\! \left(x \right) = F_{466}\! \left(x \right)+F_{470}\! \left(x \right)
F_{466}\! \left(x \right) = F_{369}\! \left(x \right)+F_{467}\! \left(x \right)
F_{467}\! \left(x \right) = F_{468}\! \left(x \right)
F_{468}\! \left(x \right) = F_{4}\! \left(x \right) F_{469}\! \left(x \right)
F_{469}\! \left(x \right) = F_{373}\! \left(x \right)
F_{470}\! \left(x \right) = F_{471}\! \left(x \right)+F_{476}\! \left(x \right)
F_{471}\! \left(x \right) = F_{472}\! \left(x \right)
F_{472}\! \left(x \right) = F_{4}\! \left(x \right) F_{473}\! \left(x \right)
F_{473}\! \left(x \right) = F_{474}\! \left(x \right)+F_{475}\! \left(x \right)
F_{474}\! \left(x \right) = F_{369}\! \left(x \right)
F_{475}\! \left(x \right) = F_{471}\! \left(x \right)
F_{476}\! \left(x \right) = F_{477}\! \left(x \right)
F_{477}\! \left(x \right) = F_{4}\! \left(x \right) F_{478}\! \left(x \right)
F_{478}\! \left(x \right) = F_{479}\! \left(x \right)+F_{480}\! \left(x \right)
F_{479}\! \left(x \right) = F_{467}\! \left(x \right)
F_{480}\! \left(x \right) = F_{481}\! \left(x \right)
F_{481}\! \left(x \right) = F_{4}\! \left(x \right) F_{482}\! \left(x \right)
F_{482}\! \left(x \right) = F_{483}\! \left(x \right)+F_{484}\! \left(x \right)
F_{483}\! \left(x \right) = F_{467}\! \left(x \right)
F_{484}\! \left(x \right) = F_{481}\! \left(x \right)
F_{485}\! \left(x \right) = F_{4}\! \left(x \right) F_{486}\! \left(x \right)
F_{486}\! \left(x \right) = F_{487}\! \left(x \right)+F_{488}\! \left(x \right)
F_{487}\! \left(x \right) = F_{412}\! \left(x \right)
F_{488}\! \left(x \right) = F_{439}\! \left(x \right)
F_{489}\! \left(x \right) = F_{4}\! \left(x \right) F_{490}\! \left(x \right)
F_{490}\! \left(x \right) = F_{491}\! \left(x \right)+F_{492}\! \left(x \right)
F_{491}\! \left(x \right) = F_{314}\! \left(x \right)+F_{412}\! \left(x \right)
F_{492}\! \left(x \right) = F_{341}\! \left(x \right)+F_{439}\! \left(x \right)
F_{493}\! \left(x \right) = F_{4}\! \left(x \right) F_{494}\! \left(x \right)
F_{494}\! \left(x \right) = F_{2}\! \left(x \right)+F_{314}\! \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_20(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))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_11(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_257(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_42(x))
Eq(F_25(x), F_26(x) + F_7(x))
Eq(F_26(x), F_22(x) + F_27(x) + F_37(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_33(x))
Eq(F_29(x), F_11(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_4(x))
Eq(F_33(x), F_17(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_30(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_14(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_4(x))
Eq(F_42(x), F_129(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_52(x))
Eq(F_46(x), F_47(x) + F_7(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_51(x))
Eq(F_50(x), F_11(x))
Eq(F_51(x), F_17(x))
Eq(F_52(x), F_43(x) + F_53(x))
Eq(F_53(x), 2*F_22(x) + F_54(x) + F_75(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_60(x))
Eq(F_56(x), F_47(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_51(x))
Eq(F_60(x), F_61(x) + F_66(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_47(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_57(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_57(x))
Eq(F_74(x), F_71(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_104(x) + F_77(x))
Eq(F_77(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_83(x))
Eq(F_81(x), F_11(x) + F_82(x))
Eq(F_82(x), F_48(x))
Eq(F_83(x), F_78(x) + F_84(x))
Eq(F_84(x), 2*F_22(x) + F_75(x) + F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_89(x))
Eq(F_87(x), F_82(x) + F_88(x))
Eq(F_88(x), F_58(x))
Eq(F_89(x), F_90(x) + F_95(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_82(x))
Eq(F_94(x), F_90(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_98(x) + F_99(x))
Eq(F_98(x), F_88(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_88(x))
Eq(F_103(x), F_100(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x) + F_127(x) + 2*F_22(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_108(x) + F_112(x))
Eq(F_108(x), F_109(x) + F_17(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_17(x))
Eq(F_112(x), F_113(x) + F_118(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_17(x))
Eq(F_117(x), F_113(x))
Eq(F_118(x), F_119(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_109(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_4(x))
Eq(F_124(x), F_125(x) + F_126(x))
Eq(F_125(x), F_109(x))
Eq(F_126(x), F_123(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_78(x))
Eq(F_129(x), F_130(x) + 2*F_22(x) + F_253(x))
Eq(F_130(x), F_131(x)*F_4(x))
Eq(F_131(x), F_132(x) + F_140(x))
Eq(F_132(x), F_133(x) + F_26(x))
Eq(F_133(x), F_134(x) + F_138(x) + 2*F_22(x))
Eq(F_134(x), F_135(x)*F_4(x))
Eq(F_135(x), F_136(x) + F_137(x))
Eq(F_136(x), F_30(x))
Eq(F_137(x), F_34(x))
Eq(F_138(x), F_139(x)*F_4(x))
Eq(F_139(x), F_33(x))
Eq(F_140(x), F_141(x) + F_227(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_143(x)*F_4(x))
Eq(F_143(x), F_144(x) + F_150(x))
Eq(F_144(x), F_145(x) + F_26(x))
Eq(F_145(x), F_146(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_30(x))
Eq(F_149(x), F_34(x))
Eq(F_150(x), F_141(x) + F_151(x))
Eq(F_151(x), F_152(x) + F_173(x) + 3*F_22(x))
Eq(F_152(x), F_153(x)*F_4(x))
Eq(F_153(x), F_154(x) + F_158(x))
Eq(F_154(x), F_145(x) + F_155(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_157(x)*F_4(x))
Eq(F_157(x), F_149(x))
Eq(F_158(x), F_159(x) + F_164(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_161(x)*F_4(x))
Eq(F_161(x), F_162(x) + F_163(x))
Eq(F_162(x), F_145(x))
Eq(F_163(x), F_159(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_166(x)*F_4(x))
Eq(F_166(x), F_167(x) + F_168(x))
Eq(F_167(x), F_155(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_170(x)*F_4(x))
Eq(F_170(x), F_171(x) + F_172(x))
Eq(F_171(x), F_155(x))
Eq(F_172(x), F_169(x))
Eq(F_173(x), F_174(x)*F_4(x))
Eq(F_174(x), F_175(x) + F_202(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_177(x))
Eq(F_177(x), F_178(x)*F_4(x))
Eq(F_178(x), F_179(x) + F_181(x))
Eq(F_179(x), F_180(x) + F_30(x))
Eq(F_180(x), F_146(x))
Eq(F_181(x), F_176(x) + F_182(x))
Eq(F_182(x), F_173(x) + F_183(x) + 3*F_22(x))
Eq(F_183(x), F_184(x)*F_4(x))
Eq(F_184(x), F_185(x) + F_187(x))
Eq(F_185(x), F_180(x) + F_186(x))
Eq(F_186(x), F_156(x))
Eq(F_187(x), F_188(x) + F_193(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_190(x)*F_4(x))
Eq(F_190(x), F_191(x) + F_192(x))
Eq(F_191(x), F_180(x))
Eq(F_192(x), F_188(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_195(x)*F_4(x))
Eq(F_195(x), F_196(x) + F_197(x))
Eq(F_196(x), F_186(x))
Eq(F_197(x), F_198(x))
Eq(F_198(x), F_199(x)*F_4(x))
Eq(F_199(x), F_200(x) + F_201(x))
Eq(F_200(x), F_186(x))
Eq(F_201(x), F_198(x))
Eq(F_202(x), F_203(x))
Eq(F_203(x), F_204(x) + 3*F_22(x) + F_225(x))
Eq(F_204(x), F_205(x)*F_4(x))
Eq(F_205(x), F_206(x) + F_210(x))
Eq(F_206(x), F_207(x) + F_34(x))
Eq(F_207(x), F_208(x))
Eq(F_208(x), F_209(x)*F_4(x))
Eq(F_209(x), F_34(x))
Eq(F_210(x), F_211(x) + F_216(x))
Eq(F_211(x), F_212(x))
Eq(F_212(x), F_213(x)*F_4(x))
Eq(F_213(x), F_214(x) + F_215(x))
Eq(F_214(x), F_34(x))
Eq(F_215(x), F_211(x))
Eq(F_216(x), F_217(x))
Eq(F_217(x), F_218(x)*F_4(x))
Eq(F_218(x), F_219(x) + F_220(x))
Eq(F_219(x), F_207(x))
Eq(F_220(x), F_221(x))
Eq(F_221(x), F_222(x)*F_4(x))
Eq(F_222(x), F_223(x) + F_224(x))
Eq(F_223(x), F_207(x))
Eq(F_224(x), F_221(x))
Eq(F_225(x), F_226(x)*F_4(x))
Eq(F_226(x), F_176(x))
Eq(F_227(x), 3*F_22(x) + F_228(x) + F_249(x))
Eq(F_228(x), F_229(x)*F_4(x))
Eq(F_229(x), F_230(x) + F_234(x))
Eq(F_230(x), F_133(x) + F_231(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_233(x)*F_4(x))
Eq(F_233(x), F_137(x))
Eq(F_234(x), F_235(x) + F_240(x))
Eq(F_235(x), F_236(x))
Eq(F_236(x), F_237(x)*F_4(x))
Eq(F_237(x), F_238(x) + F_239(x))
Eq(F_238(x), F_133(x))
Eq(F_239(x), F_235(x))
Eq(F_240(x), F_241(x))
Eq(F_241(x), F_242(x)*F_4(x))
Eq(F_242(x), F_243(x) + F_244(x))
Eq(F_243(x), F_231(x))
Eq(F_244(x), F_245(x))
Eq(F_245(x), F_246(x)*F_4(x))
Eq(F_246(x), F_247(x) + F_248(x))
Eq(F_247(x), F_231(x))
Eq(F_248(x), F_245(x))
Eq(F_249(x), F_250(x)*F_4(x))
Eq(F_250(x), F_251(x) + F_252(x))
Eq(F_251(x), F_176(x))
Eq(F_252(x), F_203(x))
Eq(F_253(x), F_254(x)*F_4(x))
Eq(F_254(x), F_255(x) + F_256(x))
Eq(F_255(x), F_176(x) + F_78(x))
Eq(F_256(x), F_105(x) + F_203(x))
Eq(F_257(x), F_258(x)*F_4(x))
Eq(F_258(x), F_259(x) + F_260(x))
Eq(F_259(x), F_2(x) + F_78(x))
Eq(F_260(x), F_105(x) + F_261(x))
Eq(F_261(x), F_22(x) + F_262(x) + F_493(x))
Eq(F_262(x), F_263(x)*F_4(x))
Eq(F_263(x), F_264(x) + F_278(x))
Eq(F_264(x), F_15(x) + F_265(x))
Eq(F_265(x), F_22(x) + F_266(x) + F_276(x))
Eq(F_266(x), F_267(x)*F_4(x))
Eq(F_267(x), F_268(x) + F_271(x))
Eq(F_268(x), F_269(x) + F_4(x))
Eq(F_269(x), F_270(x))
Eq(F_270(x), x**2)
Eq(F_271(x), F_272(x) + F_273(x))
Eq(F_272(x), F_40(x))
Eq(F_273(x), F_274(x))
Eq(F_274(x), F_275(x)*F_4(x))
Eq(F_275(x), F_269(x))
Eq(F_276(x), F_277(x)*F_4(x))
Eq(F_277(x), F_15(x) + F_272(x))
Eq(F_278(x), F_279(x) + F_365(x))
Eq(F_279(x), F_280(x))
Eq(F_280(x), F_281(x)*F_4(x))
Eq(F_281(x), F_282(x) + F_288(x))
Eq(F_282(x), F_15(x) + F_283(x))
Eq(F_283(x), F_284(x))
Eq(F_284(x), F_285(x)*F_4(x))
Eq(F_285(x), F_286(x) + F_287(x))
Eq(F_286(x), F_4(x))
Eq(F_287(x), F_272(x))
Eq(F_288(x), F_279(x) + F_289(x))
Eq(F_289(x), 2*F_22(x) + F_290(x) + F_311(x))
Eq(F_290(x), F_291(x)*F_4(x))
Eq(F_291(x), F_292(x) + F_296(x))
Eq(F_292(x), F_283(x) + F_293(x))
Eq(F_293(x), F_294(x))
Eq(F_294(x), F_295(x)*F_4(x))
Eq(F_295(x), F_287(x))
Eq(F_296(x), F_297(x) + F_302(x))
Eq(F_297(x), F_298(x))
Eq(F_298(x), F_299(x)*F_4(x))
Eq(F_299(x), F_300(x) + F_301(x))
Eq(F_300(x), F_283(x))
Eq(F_301(x), F_297(x))
Eq(F_302(x), F_303(x))
Eq(F_303(x), F_304(x)*F_4(x))
Eq(F_304(x), F_305(x) + F_306(x))
Eq(F_305(x), F_293(x))
Eq(F_306(x), F_307(x))
Eq(F_307(x), F_308(x)*F_4(x))
Eq(F_308(x), F_309(x) + F_310(x))
Eq(F_309(x), F_293(x))
Eq(F_310(x), F_307(x))
Eq(F_311(x), F_312(x)*F_4(x))
Eq(F_312(x), F_313(x) + F_340(x))
Eq(F_313(x), F_314(x))
Eq(F_314(x), F_315(x))
Eq(F_315(x), F_316(x)*F_4(x))
Eq(F_316(x), F_317(x) + F_319(x))
Eq(F_317(x), F_318(x) + F_4(x))
Eq(F_318(x), F_284(x))
Eq(F_319(x), F_314(x) + F_320(x))
Eq(F_320(x), 2*F_22(x) + F_311(x) + F_321(x))
Eq(F_321(x), F_322(x)*F_4(x))
Eq(F_322(x), F_323(x) + F_325(x))
Eq(F_323(x), F_318(x) + F_324(x))
Eq(F_324(x), F_294(x))
Eq(F_325(x), F_326(x) + F_331(x))
Eq(F_326(x), F_327(x))
Eq(F_327(x), F_328(x)*F_4(x))
Eq(F_328(x), F_329(x) + F_330(x))
Eq(F_329(x), F_318(x))
Eq(F_330(x), F_326(x))
Eq(F_331(x), F_332(x))
Eq(F_332(x), F_333(x)*F_4(x))
Eq(F_333(x), F_334(x) + F_335(x))
Eq(F_334(x), F_324(x))
Eq(F_335(x), F_336(x))
Eq(F_336(x), F_337(x)*F_4(x))
Eq(F_337(x), F_338(x) + F_339(x))
Eq(F_338(x), F_324(x))
Eq(F_339(x), F_336(x))
Eq(F_340(x), F_341(x))
Eq(F_341(x), 2*F_22(x) + F_342(x) + F_363(x))
Eq(F_342(x), F_343(x)*F_4(x))
Eq(F_343(x), F_344(x) + F_348(x))
Eq(F_344(x), F_272(x) + F_345(x))
Eq(F_345(x), F_346(x))
Eq(F_346(x), F_347(x)*F_4(x))
Eq(F_347(x), F_272(x))
Eq(F_348(x), F_349(x) + F_354(x))
Eq(F_349(x), F_350(x))
Eq(F_350(x), F_351(x)*F_4(x))
Eq(F_351(x), F_352(x) + F_353(x))
Eq(F_352(x), F_272(x))
Eq(F_353(x), F_349(x))
Eq(F_354(x), F_355(x))
Eq(F_355(x), F_356(x)*F_4(x))
Eq(F_356(x), F_357(x) + F_358(x))
Eq(F_357(x), F_345(x))
Eq(F_358(x), F_359(x))
Eq(F_359(x), F_360(x)*F_4(x))
Eq(F_360(x), F_361(x) + F_362(x))
Eq(F_361(x), F_345(x))
Eq(F_362(x), F_359(x))
Eq(F_363(x), F_364(x)*F_4(x))
Eq(F_364(x), F_314(x))
Eq(F_365(x), 2*F_22(x) + F_366(x) + F_489(x))
Eq(F_366(x), F_367(x)*F_4(x))
Eq(F_367(x), F_368(x) + F_376(x))
Eq(F_368(x), F_265(x) + F_369(x))
Eq(F_369(x), 2*F_22(x) + F_370(x) + F_374(x))
Eq(F_370(x), F_371(x)*F_4(x))
Eq(F_371(x), F_372(x) + F_373(x))
Eq(F_372(x), F_269(x))
Eq(F_373(x), F_273(x))
Eq(F_374(x), F_375(x)*F_4(x))
Eq(F_375(x), F_271(x))
Eq(F_376(x), F_377(x) + F_463(x))
Eq(F_377(x), F_378(x))
Eq(F_378(x), F_379(x)*F_4(x))
Eq(F_379(x), F_380(x) + F_386(x))
Eq(F_380(x), F_265(x) + F_381(x))
Eq(F_381(x), F_382(x))
Eq(F_382(x), F_383(x)*F_4(x))
Eq(F_383(x), F_384(x) + F_385(x))
Eq(F_384(x), F_269(x))
Eq(F_385(x), F_273(x))
Eq(F_386(x), F_377(x) + F_387(x))
Eq(F_387(x), 3*F_22(x) + F_388(x) + F_409(x))
Eq(F_388(x), F_389(x)*F_4(x))
Eq(F_389(x), F_390(x) + F_394(x))
Eq(F_390(x), F_381(x) + F_391(x))
Eq(F_391(x), F_392(x))
Eq(F_392(x), F_393(x)*F_4(x))
Eq(F_393(x), F_385(x))
Eq(F_394(x), F_395(x) + F_400(x))
Eq(F_395(x), F_396(x))
Eq(F_396(x), F_397(x)*F_4(x))
Eq(F_397(x), F_398(x) + F_399(x))
Eq(F_398(x), F_381(x))
Eq(F_399(x), F_395(x))
Eq(F_400(x), F_401(x))
Eq(F_401(x), F_4(x)*F_402(x))
Eq(F_402(x), F_403(x) + F_404(x))
Eq(F_403(x), F_391(x))
Eq(F_404(x), F_405(x))
Eq(F_405(x), F_4(x)*F_406(x))
Eq(F_406(x), F_407(x) + F_408(x))
Eq(F_407(x), F_391(x))
Eq(F_408(x), F_405(x))
Eq(F_409(x), F_4(x)*F_410(x))
Eq(F_410(x), F_411(x) + F_438(x))
Eq(F_411(x), F_412(x))
Eq(F_412(x), F_413(x))
Eq(F_413(x), F_4(x)*F_414(x))
Eq(F_414(x), F_415(x) + F_417(x))
Eq(F_415(x), F_269(x) + F_416(x))
Eq(F_416(x), F_382(x))
Eq(F_417(x), F_412(x) + F_418(x))
Eq(F_418(x), 3*F_22(x) + F_409(x) + F_419(x))
Eq(F_419(x), F_4(x)*F_420(x))
Eq(F_420(x), F_421(x) + F_423(x))
Eq(F_421(x), F_416(x) + F_422(x))
Eq(F_422(x), F_392(x))
Eq(F_423(x), F_424(x) + F_429(x))
Eq(F_424(x), F_425(x))
Eq(F_425(x), F_4(x)*F_426(x))
Eq(F_426(x), F_427(x) + F_428(x))
Eq(F_427(x), F_416(x))
Eq(F_428(x), F_424(x))
Eq(F_429(x), F_430(x))
Eq(F_430(x), F_4(x)*F_431(x))
Eq(F_431(x), F_432(x) + F_433(x))
Eq(F_432(x), F_422(x))
Eq(F_433(x), F_434(x))
Eq(F_434(x), F_4(x)*F_435(x))
Eq(F_435(x), F_436(x) + F_437(x))
Eq(F_436(x), F_422(x))
Eq(F_437(x), F_434(x))
Eq(F_438(x), F_439(x))
Eq(F_439(x), 3*F_22(x) + F_440(x) + F_461(x))
Eq(F_440(x), F_4(x)*F_441(x))
Eq(F_441(x), F_442(x) + F_446(x))
Eq(F_442(x), F_273(x) + F_443(x))
Eq(F_443(x), F_444(x))
Eq(F_444(x), F_4(x)*F_445(x))
Eq(F_445(x), F_273(x))
Eq(F_446(x), F_447(x) + F_452(x))
Eq(F_447(x), F_448(x))
Eq(F_448(x), F_4(x)*F_449(x))
Eq(F_449(x), F_450(x) + F_451(x))
Eq(F_450(x), F_273(x))
Eq(F_451(x), F_447(x))
Eq(F_452(x), F_453(x))
Eq(F_453(x), F_4(x)*F_454(x))
Eq(F_454(x), F_455(x) + F_456(x))
Eq(F_455(x), F_443(x))
Eq(F_456(x), F_457(x))
Eq(F_457(x), F_4(x)*F_458(x))
Eq(F_458(x), F_459(x) + F_460(x))
Eq(F_459(x), F_443(x))
Eq(F_460(x), F_457(x))
Eq(F_461(x), F_4(x)*F_462(x))
Eq(F_462(x), F_412(x))
Eq(F_463(x), 3*F_22(x) + F_464(x) + F_485(x))
Eq(F_464(x), F_4(x)*F_465(x))
Eq(F_465(x), F_466(x) + F_470(x))
Eq(F_466(x), F_369(x) + F_467(x))
Eq(F_467(x), F_468(x))
Eq(F_468(x), F_4(x)*F_469(x))
Eq(F_469(x), F_373(x))
Eq(F_470(x), F_471(x) + F_476(x))
Eq(F_471(x), F_472(x))
Eq(F_472(x), F_4(x)*F_473(x))
Eq(F_473(x), F_474(x) + F_475(x))
Eq(F_474(x), F_369(x))
Eq(F_475(x), F_471(x))
Eq(F_476(x), F_477(x))
Eq(F_477(x), F_4(x)*F_478(x))
Eq(F_478(x), F_479(x) + F_480(x))
Eq(F_479(x), F_467(x))
Eq(F_480(x), F_481(x))
Eq(F_481(x), F_4(x)*F_482(x))
Eq(F_482(x), F_483(x) + F_484(x))
Eq(F_483(x), F_467(x))
Eq(F_484(x), F_481(x))
Eq(F_485(x), F_4(x)*F_486(x))
Eq(F_486(x), F_487(x) + F_488(x))
Eq(F_487(x), F_412(x))
Eq(F_488(x), F_439(x))
Eq(F_489(x), F_4(x)*F_490(x))
Eq(F_490(x), F_491(x) + F_492(x))
Eq(F_491(x), F_314(x) + F_412(x))
Eq(F_492(x), F_341(x) + F_439(x))
Eq(F_493(x), F_4(x)*F_494(x))
Eq(F_494(x), F_2(x) + F_314(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": [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": [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, 2, 3, 1], "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": [2, 1, 3, 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"original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[0, 6]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 5], [1, 5]]}, {"patt": [0, 1], "pos": [[1, 5], [1, 6]]}, {"patt": [0, 1], "pos": [[1, 6], [1, 6]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 4]]}, {"patt": [1, 0], "pos": [[1, 6], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 6], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 6], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 6], [1, 4]]}, {"patt": [1, 0], "pos": [[1, 6], [1, 6]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 5]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 6]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 3], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 3], [1, 5]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 3], [1, 6]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 4], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 4], [1, 5]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 4], [1, 6]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 5]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 6]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 4], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 4], [1, 5]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 4], [1, 6]]}, {"patt": [0, 1, 2], "pos": [[1, 4], [1, 4], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 4], [1, 4], [1, 5]]}, {"patt": [0, 1, 2], "pos": [[1, 4], [1, 4], [1, 6]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 4], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [2, 1, 0], "pos": [[1, 4], [1, 3], [1, 3]]}, {"patt": [2, 1, 0], "pos": [[1, 4], [1, 4], [1, 3]]}, {"patt": [2, 1, 0], "pos": [[1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 0], "pos": [[1, 5], [1, 5], [1, 5]]}, {"patt": [2, 1, 0], "pos": [[1, 6], [1, 5], [1, 5]]}, {"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, 0], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 5]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 6]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 5]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 6]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 5]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 6]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 5]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 4], [1, 6]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"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": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}], [{"patt": [0], "pos": [[1, 4]]}], [{"patt": [0], "pos": [[1, 5]]}], [{"patt": [0], "pos": [[1, 6]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 4]]}, {"patt": [0, 1], "pos": [[0, 4], [0, 4]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 4], [0, 3], [0, 3]]}, {"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, 0], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 4]]}, {"patt": [0, 2, 3, 1], "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": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[0, 4]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0, 0, 0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_placements
Tree: http://permpal.com/tree/24353/
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[20,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[18,x] = F[19,x]*F[4,x]
F[19,x] = F[11,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[257,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[42,x]
F[25,x] = F[26,x]+F[7,x]
F[26,x] = F[22,x]+F[27,x]+F[37,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[33,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[4,x]
F[33,x] = F[17,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[30,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[14,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[4,x]
F[42,x] = F[129,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[52,x]
F[46,x] = F[47,x]+F[7,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[51,x]
F[50,x] = F[11,x]
F[51,x] = F[17,x]
F[52,x] = F[43,x]+F[53,x]
F[53,x] = 2*F[22,x]+F[54,x]+F[75,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[60,x]
F[56,x] = F[47,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[51,x]
F[60,x] = F[61,x]+F[66,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[47,x]
F[65,x] = F[61,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[57,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[57,x]
F[74,x] = F[71,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[104,x]+F[77,x]
F[77,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[83,x]
F[81,x] = F[11,x]+F[82,x]
F[82,x] = F[48,x]
F[83,x] = F[78,x]+F[84,x]
F[84,x] = 2*F[22,x]+F[75,x]+F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[87,x]+F[89,x]
F[87,x] = F[82,x]+F[88,x]
F[88,x] = F[58,x]
F[89,x] = F[90,x]+F[95,x]
F[90,x] = F[91,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[82,x]
F[94,x] = F[90,x]
F[95,x] = F[96,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[98,x]+F[99,x]
F[98,x] = F[88,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[88,x]
F[103,x] = F[100,x]
F[104,x] = F[105,x]
F[105,x] = 2*F[22,x]+F[106,x]+F[127,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[108,x]+F[112,x]
F[108,x] = F[109,x]+F[17,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[17,x]
F[112,x] = F[113,x]+F[118,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[17,x]
F[117,x] = F[113,x]
F[118,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[109,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[4,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[109,x]
F[126,x] = F[123,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[78,x]
F[129,x] = 2*F[22,x]+F[130,x]+F[253,x]
F[130,x] = F[131,x]*F[4,x]
F[131,x] = F[132,x]+F[140,x]
F[132,x] = F[133,x]+F[26,x]
F[133,x] = 2*F[22,x]+F[134,x]+F[138,x]
F[134,x] = F[135,x]*F[4,x]
F[135,x] = F[136,x]+F[137,x]
F[136,x] = F[30,x]
F[137,x] = F[34,x]
F[138,x] = F[139,x]*F[4,x]
F[139,x] = F[33,x]
F[140,x] = F[141,x]+F[227,x]
F[141,x] = F[142,x]
F[142,x] = F[143,x]*F[4,x]
F[143,x] = F[144,x]+F[150,x]
F[144,x] = F[145,x]+F[26,x]
F[145,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[30,x]
F[149,x] = F[34,x]
F[150,x] = F[141,x]+F[151,x]
F[151,x] = 3*F[22,x]+F[152,x]+F[173,x]
F[152,x] = F[153,x]*F[4,x]
F[153,x] = F[154,x]+F[158,x]
F[154,x] = F[145,x]+F[155,x]
F[155,x] = F[156,x]
F[156,x] = F[157,x]*F[4,x]
F[157,x] = F[149,x]
F[158,x] = F[159,x]+F[164,x]
F[159,x] = F[160,x]
F[160,x] = F[161,x]*F[4,x]
F[161,x] = F[162,x]+F[163,x]
F[162,x] = F[145,x]
F[163,x] = F[159,x]
F[164,x] = F[165,x]
F[165,x] = F[166,x]*F[4,x]
F[166,x] = F[167,x]+F[168,x]
F[167,x] = F[155,x]
F[168,x] = F[169,x]
F[169,x] = F[170,x]*F[4,x]
F[170,x] = F[171,x]+F[172,x]
F[171,x] = F[155,x]
F[172,x] = F[169,x]
F[173,x] = F[174,x]*F[4,x]
F[174,x] = F[175,x]+F[202,x]
F[175,x] = F[176,x]
F[176,x] = F[177,x]
F[177,x] = F[178,x]*F[4,x]
F[178,x] = F[179,x]+F[181,x]
F[179,x] = F[180,x]+F[30,x]
F[180,x] = F[146,x]
F[181,x] = F[176,x]+F[182,x]
F[182,x] = 3*F[22,x]+F[173,x]+F[183,x]
F[183,x] = F[184,x]*F[4,x]
F[184,x] = F[185,x]+F[187,x]
F[185,x] = F[180,x]+F[186,x]
F[186,x] = F[156,x]
F[187,x] = F[188,x]+F[193,x]
F[188,x] = F[189,x]
F[189,x] = F[190,x]*F[4,x]
F[190,x] = F[191,x]+F[192,x]
F[191,x] = F[180,x]
F[192,x] = F[188,x]
F[193,x] = F[194,x]
F[194,x] = F[195,x]*F[4,x]
F[195,x] = F[196,x]+F[197,x]
F[196,x] = F[186,x]
F[197,x] = F[198,x]
F[198,x] = F[199,x]*F[4,x]
F[199,x] = F[200,x]+F[201,x]
F[200,x] = F[186,x]
F[201,x] = F[198,x]
F[202,x] = F[203,x]
F[203,x] = 3*F[22,x]+F[204,x]+F[225,x]
F[204,x] = F[205,x]*F[4,x]
F[205,x] = F[206,x]+F[210,x]
F[206,x] = F[207,x]+F[34,x]
F[207,x] = F[208,x]
F[208,x] = F[209,x]*F[4,x]
F[209,x] = F[34,x]
F[210,x] = F[211,x]+F[216,x]
F[211,x] = F[212,x]
F[212,x] = F[213,x]*F[4,x]
F[213,x] = F[214,x]+F[215,x]
F[214,x] = F[34,x]
F[215,x] = F[211,x]
F[216,x] = F[217,x]
F[217,x] = F[218,x]*F[4,x]
F[218,x] = F[219,x]+F[220,x]
F[219,x] = F[207,x]
F[220,x] = F[221,x]
F[221,x] = F[222,x]*F[4,x]
F[222,x] = F[223,x]+F[224,x]
F[223,x] = F[207,x]
F[224,x] = F[221,x]
F[225,x] = F[226,x]*F[4,x]
F[226,x] = F[176,x]
F[227,x] = 3*F[22,x]+F[228,x]+F[249,x]
F[228,x] = F[229,x]*F[4,x]
F[229,x] = F[230,x]+F[234,x]
F[230,x] = F[133,x]+F[231,x]
F[231,x] = F[232,x]
F[232,x] = F[233,x]*F[4,x]
F[233,x] = F[137,x]
F[234,x] = F[235,x]+F[240,x]
F[235,x] = F[236,x]
F[236,x] = F[237,x]*F[4,x]
F[237,x] = F[238,x]+F[239,x]
F[238,x] = F[133,x]
F[239,x] = F[235,x]
F[240,x] = F[241,x]
F[241,x] = F[242,x]*F[4,x]
F[242,x] = F[243,x]+F[244,x]
F[243,x] = F[231,x]
F[244,x] = F[245,x]
F[245,x] = F[246,x]*F[4,x]
F[246,x] = F[247,x]+F[248,x]
F[247,x] = F[231,x]
F[248,x] = F[245,x]
F[249,x] = F[250,x]*F[4,x]
F[250,x] = F[251,x]+F[252,x]
F[251,x] = F[176,x]
F[252,x] = F[203,x]
F[253,x] = F[254,x]*F[4,x]
F[254,x] = F[255,x]+F[256,x]
F[255,x] = F[176,x]+F[78,x]
F[256,x] = F[105,x]+F[203,x]
F[257,x] = F[258,x]*F[4,x]
F[258,x] = F[259,x]+F[260,x]
F[259,x] = F[2,x]+F[78,x]
F[260,x] = F[105,x]+F[261,x]
F[261,x] = F[22,x]+F[262,x]+F[493,x]
F[262,x] = F[263,x]*F[4,x]
F[263,x] = F[264,x]+F[278,x]
F[264,x] = F[15,x]+F[265,x]
F[265,x] = F[22,x]+F[266,x]+F[276,x]
F[266,x] = F[267,x]*F[4,x]
F[267,x] = F[268,x]+F[271,x]
F[268,x] = F[269,x]+F[4,x]
F[269,x] = F[270,x]
F[270,x] = x^2
F[271,x] = F[272,x]+F[273,x]
F[272,x] = F[40,x]
F[273,x] = F[274,x]
F[274,x] = F[275,x]*F[4,x]
F[275,x] = F[269,x]
F[276,x] = F[277,x]*F[4,x]
F[277,x] = F[15,x]+F[272,x]
F[278,x] = F[279,x]+F[365,x]
F[279,x] = F[280,x]
F[280,x] = F[281,x]*F[4,x]
F[281,x] = F[282,x]+F[288,x]
F[282,x] = F[15,x]+F[283,x]
F[283,x] = F[284,x]
F[284,x] = F[285,x]*F[4,x]
F[285,x] = F[286,x]+F[287,x]
F[286,x] = F[4,x]
F[287,x] = F[272,x]
F[288,x] = F[279,x]+F[289,x]
F[289,x] = 2*F[22,x]+F[290,x]+F[311,x]
F[290,x] = F[291,x]*F[4,x]
F[291,x] = F[292,x]+F[296,x]
F[292,x] = F[283,x]+F[293,x]
F[293,x] = F[294,x]
F[294,x] = F[295,x]*F[4,x]
F[295,x] = F[287,x]
F[296,x] = F[297,x]+F[302,x]
F[297,x] = F[298,x]
F[298,x] = F[299,x]*F[4,x]
F[299,x] = F[300,x]+F[301,x]
F[300,x] = F[283,x]
F[301,x] = F[297,x]
F[302,x] = F[303,x]
F[303,x] = F[304,x]*F[4,x]
F[304,x] = F[305,x]+F[306,x]
F[305,x] = F[293,x]
F[306,x] = F[307,x]
F[307,x] = F[308,x]*F[4,x]
F[308,x] = F[309,x]+F[310,x]
F[309,x] = F[293,x]
F[310,x] = F[307,x]
F[311,x] = F[312,x]*F[4,x]
F[312,x] = F[313,x]+F[340,x]
F[313,x] = F[314,x]
F[314,x] = F[315,x]
F[315,x] = F[316,x]*F[4,x]
F[316,x] = F[317,x]+F[319,x]
F[317,x] = F[318,x]+F[4,x]
F[318,x] = F[284,x]
F[319,x] = F[314,x]+F[320,x]
F[320,x] = 2*F[22,x]+F[311,x]+F[321,x]
F[321,x] = F[322,x]*F[4,x]
F[322,x] = F[323,x]+F[325,x]
F[323,x] = F[318,x]+F[324,x]
F[324,x] = F[294,x]
F[325,x] = F[326,x]+F[331,x]
F[326,x] = F[327,x]
F[327,x] = F[328,x]*F[4,x]
F[328,x] = F[329,x]+F[330,x]
F[329,x] = F[318,x]
F[330,x] = F[326,x]
F[331,x] = F[332,x]
F[332,x] = F[333,x]*F[4,x]
F[333,x] = F[334,x]+F[335,x]
F[334,x] = F[324,x]
F[335,x] = F[336,x]
F[336,x] = F[337,x]*F[4,x]
F[337,x] = F[338,x]+F[339,x]
F[338,x] = F[324,x]
F[339,x] = F[336,x]
F[340,x] = F[341,x]
F[341,x] = 2*F[22,x]+F[342,x]+F[363,x]
F[342,x] = F[343,x]*F[4,x]
F[343,x] = F[344,x]+F[348,x]
F[344,x] = F[272,x]+F[345,x]
F[345,x] = F[346,x]
F[346,x] = F[347,x]*F[4,x]
F[347,x] = F[272,x]
F[348,x] = F[349,x]+F[354,x]
F[349,x] = F[350,x]
F[350,x] = F[351,x]*F[4,x]
F[351,x] = F[352,x]+F[353,x]
F[352,x] = F[272,x]
F[353,x] = F[349,x]
F[354,x] = F[355,x]
F[355,x] = F[356,x]*F[4,x]
F[356,x] = F[357,x]+F[358,x]
F[357,x] = F[345,x]
F[358,x] = F[359,x]
F[359,x] = F[360,x]*F[4,x]
F[360,x] = F[361,x]+F[362,x]
F[361,x] = F[345,x]
F[362,x] = F[359,x]
F[363,x] = F[364,x]*F[4,x]
F[364,x] = F[314,x]
F[365,x] = 2*F[22,x]+F[366,x]+F[489,x]
F[366,x] = F[367,x]*F[4,x]
F[367,x] = F[368,x]+F[376,x]
F[368,x] = F[265,x]+F[369,x]
F[369,x] = 2*F[22,x]+F[370,x]+F[374,x]
F[370,x] = F[371,x]*F[4,x]
F[371,x] = F[372,x]+F[373,x]
F[372,x] = F[269,x]
F[373,x] = F[273,x]
F[374,x] = F[375,x]*F[4,x]
F[375,x] = F[271,x]
F[376,x] = F[377,x]+F[463,x]
F[377,x] = F[378,x]
F[378,x] = F[379,x]*F[4,x]
F[379,x] = F[380,x]+F[386,x]
F[380,x] = F[265,x]+F[381,x]
F[381,x] = F[382,x]
F[382,x] = F[383,x]*F[4,x]
F[383,x] = F[384,x]+F[385,x]
F[384,x] = F[269,x]
F[385,x] = F[273,x]
F[386,x] = F[377,x]+F[387,x]
F[387,x] = 3*F[22,x]+F[388,x]+F[409,x]
F[388,x] = F[389,x]*F[4,x]
F[389,x] = F[390,x]+F[394,x]
F[390,x] = F[381,x]+F[391,x]
F[391,x] = F[392,x]
F[392,x] = F[393,x]*F[4,x]
F[393,x] = F[385,x]
F[394,x] = F[395,x]+F[400,x]
F[395,x] = F[396,x]
F[396,x] = F[397,x]*F[4,x]
F[397,x] = F[398,x]+F[399,x]
F[398,x] = F[381,x]
F[399,x] = F[395,x]
F[400,x] = F[401,x]
F[401,x] = F[4,x]*F[402,x]
F[402,x] = F[403,x]+F[404,x]
F[403,x] = F[391,x]
F[404,x] = F[405,x]
F[405,x] = F[4,x]*F[406,x]
F[406,x] = F[407,x]+F[408,x]
F[407,x] = F[391,x]
F[408,x] = F[405,x]
F[409,x] = F[4,x]*F[410,x]
F[410,x] = F[411,x]+F[438,x]
F[411,x] = F[412,x]
F[412,x] = F[413,x]
F[413,x] = F[4,x]*F[414,x]
F[414,x] = F[415,x]+F[417,x]
F[415,x] = F[269,x]+F[416,x]
F[416,x] = F[382,x]
F[417,x] = F[412,x]+F[418,x]
F[418,x] = 3*F[22,x]+F[409,x]+F[419,x]
F[419,x] = F[4,x]*F[420,x]
F[420,x] = F[421,x]+F[423,x]
F[421,x] = F[416,x]+F[422,x]
F[422,x] = F[392,x]
F[423,x] = F[424,x]+F[429,x]
F[424,x] = F[425,x]
F[425,x] = F[4,x]*F[426,x]
F[426,x] = F[427,x]+F[428,x]
F[427,x] = F[416,x]
F[428,x] = F[424,x]
F[429,x] = F[430,x]
F[430,x] = F[4,x]*F[431,x]
F[431,x] = F[432,x]+F[433,x]
F[432,x] = F[422,x]
F[433,x] = F[434,x]
F[434,x] = F[4,x]*F[435,x]
F[435,x] = F[436,x]+F[437,x]
F[436,x] = F[422,x]
F[437,x] = F[434,x]
F[438,x] = F[439,x]
F[439,x] = 3*F[22,x]+F[440,x]+F[461,x]
F[440,x] = F[4,x]*F[441,x]
F[441,x] = F[442,x]+F[446,x]
F[442,x] = F[273,x]+F[443,x]
F[443,x] = F[444,x]
F[444,x] = F[4,x]*F[445,x]
F[445,x] = F[273,x]
F[446,x] = F[447,x]+F[452,x]
F[447,x] = F[448,x]
F[448,x] = F[4,x]*F[449,x]
F[449,x] = F[450,x]+F[451,x]
F[450,x] = F[273,x]
F[451,x] = F[447,x]
F[452,x] = F[453,x]
F[453,x] = F[4,x]*F[454,x]
F[454,x] = F[455,x]+F[456,x]
F[455,x] = F[443,x]
F[456,x] = F[457,x]
F[457,x] = F[4,x]*F[458,x]
F[458,x] = F[459,x]+F[460,x]
F[459,x] = F[443,x]
F[460,x] = F[457,x]
F[461,x] = F[4,x]*F[462,x]
F[462,x] = F[412,x]
F[463,x] = 3*F[22,x]+F[464,x]+F[485,x]
F[464,x] = F[4,x]*F[465,x]
F[465,x] = F[466,x]+F[470,x]
F[466,x] = F[369,x]+F[467,x]
F[467,x] = F[468,x]
F[468,x] = F[4,x]*F[469,x]
F[469,x] = F[373,x]
F[470,x] = F[471,x]+F[476,x]
F[471,x] = F[472,x]
F[472,x] = F[4,x]*F[473,x]
F[473,x] = F[474,x]+F[475,x]
F[474,x] = F[369,x]
F[475,x] = F[471,x]
F[476,x] = F[477,x]
F[477,x] = F[4,x]*F[478,x]
F[478,x] = F[479,x]+F[480,x]
F[479,x] = F[467,x]
F[480,x] = F[481,x]
F[481,x] = F[4,x]*F[482,x]
F[482,x] = F[483,x]+F[484,x]
F[483,x] = F[467,x]
F[484,x] = F[481,x]
F[485,x] = F[4,x]*F[486,x]
F[486,x] = F[487,x]+F[488,x]
F[487,x] = F[412,x]
F[488,x] = F[439,x]
F[489,x] = F[4,x]*F[490,x]
F[490,x] = F[491,x]+F[492,x]
F[491,x] = F[314,x]+F[412,x]
F[492,x] = F[341,x]+F[439,x]
F[493,x] = F[4,x]*F[494,x]
F[494,x] = F[2,x]+F[314,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_{20}\! \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_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{257}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{42}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{7}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{37}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{30}\! \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_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{17}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{129}\! \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_{52}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{7}\! \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_{51}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right)
F_{51}\! \left(x \right) = F_{17}\! \left(x \right)
F_{52}\! \left(x \right) = F_{43}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{54}\! \left(x \right)+F_{75}\! \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_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{47}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{51}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{66}\! \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_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{47}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{57}\! \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_{57}\! \left(x \right)
F_{74}\! \left(x \right) = F_{71}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{104}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \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_{83}\! \left(x \right)
F_{81}\! \left(x \right) = F_{11}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{48}\! \left(x \right)
F_{83}\! \left(x \right) = F_{78}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{75}\! \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_{89}\! \left(x \right)
F_{87}\! \left(x \right) = F_{82}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{58}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{95}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{82}\! \left(x \right)
F_{94}\! \left(x \right) = F_{90}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)+F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{88}\! \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_{88}\! \left(x \right)
F_{103}\! \left(x \right) = F_{100}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{106}\! \left(x \right)+F_{127}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{112}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{17}\! \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_{17}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{118}\! \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_{17}\! \left(x \right)
F_{117}\! \left(x \right) = F_{113}\! \left(x \right)
F_{118}\! \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_{109}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{4}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{126}\! \left(x \right)
F_{125}\! \left(x \right) = F_{109}\! \left(x \right)
F_{126}\! \left(x \right) = F_{123}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = F_{78}\! \left(x \right)
F_{129}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{130}\! \left(x \right)+F_{253}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{4}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{140}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{26}\! \left(x \right)
F_{133}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{134}\! \left(x \right)+F_{138}\! \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_{137}\! \left(x \right)
F_{136}\! \left(x \right) = F_{30}\! \left(x \right)
F_{137}\! \left(x \right) = F_{34}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{4}\! \left(x \right)
F_{139}\! \left(x \right) = F_{33}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{227}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \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_{150}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{26}\! \left(x \right)
F_{145}\! \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_{30}\! \left(x \right)
F_{149}\! \left(x \right) = F_{34}\! \left(x \right)
F_{150}\! \left(x \right) = F_{141}\! \left(x \right)+F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{152}\! \left(x \right)+F_{173}\! \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_{158}\! \left(x \right)
F_{154}\! \left(x \right) = F_{145}\! \left(x \right)+F_{155}\! \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_{149}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{164}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \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_{163}\! \left(x \right)
F_{162}\! \left(x \right) = F_{145}\! \left(x \right)
F_{163}\! \left(x \right) = F_{159}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{4}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{168}\! \left(x \right)
F_{167}\! \left(x \right) = F_{155}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right) F_{4}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)+F_{172}\! \left(x \right)
F_{171}\! \left(x \right) = F_{155}\! \left(x \right)
F_{172}\! \left(x \right) = F_{169}\! \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_{202}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \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_{181}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{30}\! \left(x \right)
F_{180}\! \left(x \right) = F_{146}\! \left(x \right)
F_{181}\! \left(x \right) = F_{176}\! \left(x \right)+F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{173}\! \left(x \right)+F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right) F_{4}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{187}\! \left(x \right)
F_{185}\! \left(x \right) = F_{180}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{156}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{193}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right) F_{4}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{192}\! \left(x \right)
F_{191}\! \left(x \right) = F_{180}\! \left(x \right)
F_{192}\! \left(x \right) = F_{188}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right) F_{4}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)+F_{197}\! \left(x \right)
F_{196}\! \left(x \right) = F_{186}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right) F_{4}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)+F_{201}\! \left(x \right)
F_{200}\! \left(x \right) = F_{186}\! \left(x \right)
F_{201}\! \left(x \right) = F_{198}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{204}\! \left(x \right)+F_{225}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right) F_{4}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)+F_{210}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)+F_{34}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right) F_{4}\! \left(x \right)
F_{209}\! \left(x \right) = F_{34}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{216}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right) F_{4}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right)+F_{215}\! \left(x \right)
F_{214}\! \left(x \right) = F_{34}\! \left(x \right)
F_{215}\! \left(x \right) = F_{211}\! \left(x \right)
F_{216}\! \left(x \right) = F_{217}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right) F_{4}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right)+F_{220}\! \left(x \right)
F_{219}\! \left(x \right) = F_{207}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right) F_{4}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right)+F_{224}\! \left(x \right)
F_{223}\! \left(x \right) = F_{207}\! \left(x \right)
F_{224}\! \left(x \right) = F_{221}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right) F_{4}\! \left(x \right)
F_{226}\! \left(x \right) = F_{176}\! \left(x \right)
F_{227}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{228}\! \left(x \right)+F_{249}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right) F_{4}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)+F_{234}\! \left(x \right)
F_{230}\! \left(x \right) = F_{133}\! \left(x \right)+F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right) F_{4}\! \left(x \right)
F_{233}\! \left(x \right) = F_{137}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)+F_{240}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right) F_{4}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)+F_{239}\! \left(x \right)
F_{238}\! \left(x \right) = F_{133}\! \left(x \right)
F_{239}\! \left(x \right) = F_{235}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right) F_{4}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)+F_{244}\! \left(x \right)
F_{243}\! \left(x \right) = F_{231}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{246}\! \left(x \right) F_{4}\! \left(x \right)
F_{246}\! \left(x \right) = F_{247}\! \left(x \right)+F_{248}\! \left(x \right)
F_{247}\! \left(x \right) = F_{231}\! \left(x \right)
F_{248}\! \left(x \right) = F_{245}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right) F_{4}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right)+F_{252}\! \left(x \right)
F_{251}\! \left(x \right) = F_{176}\! \left(x \right)
F_{252}\! \left(x \right) = F_{203}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right) F_{4}\! \left(x \right)
F_{254}\! \left(x \right) = F_{255}\! \left(x \right)+F_{256}\! \left(x \right)
F_{255}\! \left(x \right) = F_{176}\! \left(x \right)+F_{78}\! \left(x \right)
F_{256}\! \left(x \right) = F_{105}\! \left(x \right)+F_{203}\! \left(x \right)
F_{257}\! \left(x \right) = F_{258}\! \left(x \right) F_{4}\! \left(x \right)
F_{258}\! \left(x \right) = F_{259}\! \left(x \right)+F_{260}\! \left(x \right)
F_{259}\! \left(x \right) = F_{2}\! \left(x \right)+F_{78}\! \left(x \right)
F_{260}\! \left(x \right) = F_{105}\! \left(x \right)+F_{261}\! \left(x \right)
F_{261}\! \left(x \right) = F_{22}\! \left(x \right)+F_{262}\! \left(x \right)+F_{493}\! \left(x \right)
F_{262}\! \left(x \right) = F_{263}\! \left(x \right) F_{4}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right)+F_{278}\! \left(x \right)
F_{264}\! \left(x \right) = F_{15}\! \left(x \right)+F_{265}\! \left(x \right)
F_{265}\! \left(x \right) = F_{22}\! \left(x \right)+F_{266}\! \left(x \right)+F_{276}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right) F_{4}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right)+F_{271}\! \left(x \right)
F_{268}\! \left(x \right) = F_{269}\! \left(x \right)+F_{4}\! \left(x \right)
F_{269}\! \left(x \right) = F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = x^{2}
F_{271}\! \left(x \right) = F_{272}\! \left(x \right)+F_{273}\! \left(x \right)
F_{272}\! \left(x \right) = F_{40}\! \left(x \right)
F_{273}\! \left(x \right) = F_{274}\! \left(x \right)
F_{274}\! \left(x \right) = F_{275}\! \left(x \right) F_{4}\! \left(x \right)
F_{275}\! \left(x \right) = F_{269}\! \left(x \right)
F_{276}\! \left(x \right) = F_{277}\! \left(x \right) F_{4}\! \left(x \right)
F_{277}\! \left(x \right) = F_{15}\! \left(x \right)+F_{272}\! \left(x \right)
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)+F_{365}\! \left(x \right)
F_{279}\! \left(x \right) = F_{280}\! \left(x \right)
F_{280}\! \left(x \right) = F_{281}\! \left(x \right) F_{4}\! \left(x \right)
F_{281}\! \left(x \right) = F_{282}\! \left(x \right)+F_{288}\! \left(x \right)
F_{282}\! \left(x \right) = F_{15}\! \left(x \right)+F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = F_{285}\! \left(x \right) F_{4}\! \left(x \right)
F_{285}\! \left(x \right) = F_{286}\! \left(x \right)+F_{287}\! \left(x \right)
F_{286}\! \left(x \right) = F_{4}\! \left(x \right)
F_{287}\! \left(x \right) = F_{272}\! \left(x \right)
F_{288}\! \left(x \right) = F_{279}\! \left(x \right)+F_{289}\! \left(x \right)
F_{289}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{290}\! \left(x \right)+F_{311}\! \left(x \right)
F_{290}\! \left(x \right) = F_{291}\! \left(x \right) F_{4}\! \left(x \right)
F_{291}\! \left(x \right) = F_{292}\! \left(x \right)+F_{296}\! \left(x \right)
F_{292}\! \left(x \right) = F_{283}\! \left(x \right)+F_{293}\! \left(x \right)
F_{293}\! \left(x \right) = F_{294}\! \left(x \right)
F_{294}\! \left(x \right) = F_{295}\! \left(x \right) F_{4}\! \left(x \right)
F_{295}\! \left(x \right) = F_{287}\! \left(x \right)
F_{296}\! \left(x \right) = F_{297}\! \left(x \right)+F_{302}\! \left(x \right)
F_{297}\! \left(x \right) = F_{298}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right) F_{4}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)+F_{301}\! \left(x \right)
F_{300}\! \left(x \right) = F_{283}\! \left(x \right)
F_{301}\! \left(x \right) = F_{297}\! \left(x \right)
F_{302}\! \left(x \right) = F_{303}\! \left(x \right)
F_{303}\! \left(x \right) = F_{304}\! \left(x \right) F_{4}\! \left(x \right)
F_{304}\! \left(x \right) = F_{305}\! \left(x \right)+F_{306}\! \left(x \right)
F_{305}\! \left(x \right) = F_{293}\! \left(x \right)
F_{306}\! \left(x \right) = F_{307}\! \left(x \right)
F_{307}\! \left(x \right) = F_{308}\! \left(x \right) F_{4}\! \left(x \right)
F_{308}\! \left(x \right) = F_{309}\! \left(x \right)+F_{310}\! \left(x \right)
F_{309}\! \left(x \right) = F_{293}\! \left(x \right)
F_{310}\! \left(x \right) = F_{307}\! \left(x \right)
F_{311}\! \left(x \right) = F_{312}\! \left(x \right) F_{4}\! \left(x \right)
F_{312}\! \left(x \right) = F_{313}\! \left(x \right)+F_{340}\! \left(x \right)
F_{313}\! \left(x \right) = F_{314}\! \left(x \right)
F_{314}\! \left(x \right) = F_{315}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right) F_{4}\! \left(x \right)
F_{316}\! \left(x \right) = F_{317}\! \left(x \right)+F_{319}\! \left(x \right)
F_{317}\! \left(x \right) = F_{318}\! \left(x \right)+F_{4}\! \left(x \right)
F_{318}\! \left(x \right) = F_{284}\! \left(x \right)
F_{319}\! \left(x \right) = F_{314}\! \left(x \right)+F_{320}\! \left(x \right)
F_{320}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{311}\! \left(x \right)+F_{321}\! \left(x \right)
F_{321}\! \left(x \right) = F_{322}\! \left(x \right) F_{4}\! \left(x \right)
F_{322}\! \left(x \right) = F_{323}\! \left(x \right)+F_{325}\! \left(x \right)
F_{323}\! \left(x \right) = F_{318}\! \left(x \right)+F_{324}\! \left(x \right)
F_{324}\! \left(x \right) = F_{294}\! \left(x \right)
F_{325}\! \left(x \right) = F_{326}\! \left(x \right)+F_{331}\! \left(x \right)
F_{326}\! \left(x \right) = F_{327}\! \left(x \right)
F_{327}\! \left(x \right) = F_{328}\! \left(x \right) F_{4}\! \left(x \right)
F_{328}\! \left(x \right) = F_{329}\! \left(x \right)+F_{330}\! \left(x \right)
F_{329}\! \left(x \right) = F_{318}\! \left(x \right)
F_{330}\! \left(x \right) = F_{326}\! \left(x \right)
F_{331}\! \left(x \right) = F_{332}\! \left(x \right)
F_{332}\! \left(x \right) = F_{333}\! \left(x \right) F_{4}\! \left(x \right)
F_{333}\! \left(x \right) = F_{334}\! \left(x \right)+F_{335}\! \left(x \right)
F_{334}\! \left(x \right) = F_{324}\! \left(x \right)
F_{335}\! \left(x \right) = F_{336}\! \left(x \right)
F_{336}\! \left(x \right) = F_{337}\! \left(x \right) F_{4}\! \left(x \right)
F_{337}\! \left(x \right) = F_{338}\! \left(x \right)+F_{339}\! \left(x \right)
F_{338}\! \left(x \right) = F_{324}\! \left(x \right)
F_{339}\! \left(x \right) = F_{336}\! \left(x \right)
F_{340}\! \left(x \right) = F_{341}\! \left(x \right)
F_{341}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{342}\! \left(x \right)+F_{363}\! \left(x \right)
F_{342}\! \left(x \right) = F_{343}\! \left(x \right) F_{4}\! \left(x \right)
F_{343}\! \left(x \right) = F_{344}\! \left(x \right)+F_{348}\! \left(x \right)
F_{344}\! \left(x \right) = F_{272}\! \left(x \right)+F_{345}\! \left(x \right)
F_{345}\! \left(x \right) = F_{346}\! \left(x \right)
F_{346}\! \left(x \right) = F_{347}\! \left(x \right) F_{4}\! \left(x \right)
F_{347}\! \left(x \right) = F_{272}\! \left(x \right)
F_{348}\! \left(x \right) = F_{349}\! \left(x \right)+F_{354}\! \left(x \right)
F_{349}\! \left(x \right) = F_{350}\! \left(x \right)
F_{350}\! \left(x \right) = F_{351}\! \left(x \right) F_{4}\! \left(x \right)
F_{351}\! \left(x \right) = F_{352}\! \left(x \right)+F_{353}\! \left(x \right)
F_{352}\! \left(x \right) = F_{272}\! \left(x \right)
F_{353}\! \left(x \right) = F_{349}\! \left(x \right)
F_{354}\! \left(x \right) = F_{355}\! \left(x \right)
F_{355}\! \left(x \right) = F_{356}\! \left(x \right) F_{4}\! \left(x \right)
F_{356}\! \left(x \right) = F_{357}\! \left(x \right)+F_{358}\! \left(x \right)
F_{357}\! \left(x \right) = F_{345}\! \left(x \right)
F_{358}\! \left(x \right) = F_{359}\! \left(x \right)
F_{359}\! \left(x \right) = F_{360}\! \left(x \right) F_{4}\! \left(x \right)
F_{360}\! \left(x \right) = F_{361}\! \left(x \right)+F_{362}\! \left(x \right)
F_{361}\! \left(x \right) = F_{345}\! \left(x \right)
F_{362}\! \left(x \right) = F_{359}\! \left(x \right)
F_{363}\! \left(x \right) = F_{364}\! \left(x \right) F_{4}\! \left(x \right)
F_{364}\! \left(x \right) = F_{314}\! \left(x \right)
F_{365}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{366}\! \left(x \right)+F_{489}\! \left(x \right)
F_{366}\! \left(x \right) = F_{367}\! \left(x \right) F_{4}\! \left(x \right)
F_{367}\! \left(x \right) = F_{368}\! \left(x \right)+F_{376}\! \left(x \right)
F_{368}\! \left(x \right) = F_{265}\! \left(x \right)+F_{369}\! \left(x \right)
F_{369}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{370}\! \left(x \right)+F_{374}\! \left(x \right)
F_{370}\! \left(x \right) = F_{371}\! \left(x \right) F_{4}\! \left(x \right)
F_{371}\! \left(x \right) = F_{372}\! \left(x \right)+F_{373}\! \left(x \right)
F_{372}\! \left(x \right) = F_{269}\! \left(x \right)
F_{373}\! \left(x \right) = F_{273}\! \left(x \right)
F_{374}\! \left(x \right) = F_{375}\! \left(x \right) F_{4}\! \left(x \right)
F_{375}\! \left(x \right) = F_{271}\! \left(x \right)
F_{376}\! \left(x \right) = F_{377}\! \left(x \right)+F_{463}\! \left(x \right)
F_{377}\! \left(x \right) = F_{378}\! \left(x \right)
F_{378}\! \left(x \right) = F_{379}\! \left(x \right) F_{4}\! \left(x \right)
F_{379}\! \left(x \right) = F_{380}\! \left(x \right)+F_{386}\! \left(x \right)
F_{380}\! \left(x \right) = F_{265}\! \left(x \right)+F_{381}\! \left(x \right)
F_{381}\! \left(x \right) = F_{382}\! \left(x \right)
F_{382}\! \left(x \right) = F_{383}\! \left(x \right) F_{4}\! \left(x \right)
F_{383}\! \left(x \right) = F_{384}\! \left(x \right)+F_{385}\! \left(x \right)
F_{384}\! \left(x \right) = F_{269}\! \left(x \right)
F_{385}\! \left(x \right) = F_{273}\! \left(x \right)
F_{386}\! \left(x \right) = F_{377}\! \left(x \right)+F_{387}\! \left(x \right)
F_{387}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{388}\! \left(x \right)+F_{409}\! \left(x \right)
F_{388}\! \left(x \right) = F_{389}\! \left(x \right) F_{4}\! \left(x \right)
F_{389}\! \left(x \right) = F_{390}\! \left(x \right)+F_{394}\! \left(x \right)
F_{390}\! \left(x \right) = F_{381}\! \left(x \right)+F_{391}\! \left(x \right)
F_{391}\! \left(x \right) = F_{392}\! \left(x \right)
F_{392}\! \left(x \right) = F_{393}\! \left(x \right) F_{4}\! \left(x \right)
F_{393}\! \left(x \right) = F_{385}\! \left(x \right)
F_{394}\! \left(x \right) = F_{395}\! \left(x \right)+F_{400}\! \left(x \right)
F_{395}\! \left(x \right) = F_{396}\! \left(x \right)
F_{396}\! \left(x \right) = F_{397}\! \left(x \right) F_{4}\! \left(x \right)
F_{397}\! \left(x \right) = F_{398}\! \left(x \right)+F_{399}\! \left(x \right)
F_{398}\! \left(x \right) = F_{381}\! \left(x \right)
F_{399}\! \left(x \right) = F_{395}\! \left(x \right)
F_{400}\! \left(x \right) = F_{401}\! \left(x \right)
F_{401}\! \left(x \right) = F_{4}\! \left(x \right) F_{402}\! \left(x \right)
F_{402}\! \left(x \right) = F_{403}\! \left(x \right)+F_{404}\! \left(x \right)
F_{403}\! \left(x \right) = F_{391}\! \left(x \right)
F_{404}\! \left(x \right) = F_{405}\! \left(x \right)
F_{405}\! \left(x \right) = F_{4}\! \left(x \right) F_{406}\! \left(x \right)
F_{406}\! \left(x \right) = F_{407}\! \left(x \right)+F_{408}\! \left(x \right)
F_{407}\! \left(x \right) = F_{391}\! \left(x \right)
F_{408}\! \left(x \right) = F_{405}\! \left(x \right)
F_{409}\! \left(x \right) = F_{4}\! \left(x \right) F_{410}\! \left(x \right)
F_{410}\! \left(x \right) = F_{411}\! \left(x \right)+F_{438}\! \left(x \right)
F_{411}\! \left(x \right) = F_{412}\! \left(x \right)
F_{412}\! \left(x \right) = F_{413}\! \left(x \right)
F_{413}\! \left(x \right) = F_{4}\! \left(x \right) F_{414}\! \left(x \right)
F_{414}\! \left(x \right) = F_{415}\! \left(x \right)+F_{417}\! \left(x \right)
F_{415}\! \left(x \right) = F_{269}\! \left(x \right)+F_{416}\! \left(x \right)
F_{416}\! \left(x \right) = F_{382}\! \left(x \right)
F_{417}\! \left(x \right) = F_{412}\! \left(x \right)+F_{418}\! \left(x \right)
F_{418}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{409}\! \left(x \right)+F_{419}\! \left(x \right)
F_{419}\! \left(x \right) = F_{4}\! \left(x \right) F_{420}\! \left(x \right)
F_{420}\! \left(x \right) = F_{421}\! \left(x \right)+F_{423}\! \left(x \right)
F_{421}\! \left(x \right) = F_{416}\! \left(x \right)+F_{422}\! \left(x \right)
F_{422}\! \left(x \right) = F_{392}\! \left(x \right)
F_{423}\! \left(x \right) = F_{424}\! \left(x \right)+F_{429}\! \left(x \right)
F_{424}\! \left(x \right) = F_{425}\! \left(x \right)
F_{425}\! \left(x \right) = F_{4}\! \left(x \right) F_{426}\! \left(x \right)
F_{426}\! \left(x \right) = F_{427}\! \left(x \right)+F_{428}\! \left(x \right)
F_{427}\! \left(x \right) = F_{416}\! \left(x \right)
F_{428}\! \left(x \right) = F_{424}\! \left(x \right)
F_{429}\! \left(x \right) = F_{430}\! \left(x \right)
F_{430}\! \left(x \right) = F_{4}\! \left(x \right) F_{431}\! \left(x \right)
F_{431}\! \left(x \right) = F_{432}\! \left(x \right)+F_{433}\! \left(x \right)
F_{432}\! \left(x \right) = F_{422}\! \left(x \right)
F_{433}\! \left(x \right) = F_{434}\! \left(x \right)
F_{434}\! \left(x \right) = F_{4}\! \left(x \right) F_{435}\! \left(x \right)
F_{435}\! \left(x \right) = F_{436}\! \left(x \right)+F_{437}\! \left(x \right)
F_{436}\! \left(x \right) = F_{422}\! \left(x \right)
F_{437}\! \left(x \right) = F_{434}\! \left(x \right)
F_{438}\! \left(x \right) = F_{439}\! \left(x \right)
F_{439}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{440}\! \left(x \right)+F_{461}\! \left(x \right)
F_{440}\! \left(x \right) = F_{4}\! \left(x \right) F_{441}\! \left(x \right)
F_{441}\! \left(x \right) = F_{442}\! \left(x \right)+F_{446}\! \left(x \right)
F_{442}\! \left(x \right) = F_{273}\! \left(x \right)+F_{443}\! \left(x \right)
F_{443}\! \left(x \right) = F_{444}\! \left(x \right)
F_{444}\! \left(x \right) = F_{4}\! \left(x \right) F_{445}\! \left(x \right)
F_{445}\! \left(x \right) = F_{273}\! \left(x \right)
F_{446}\! \left(x \right) = F_{447}\! \left(x \right)+F_{452}\! \left(x \right)
F_{447}\! \left(x \right) = F_{448}\! \left(x \right)
F_{448}\! \left(x \right) = F_{4}\! \left(x \right) F_{449}\! \left(x \right)
F_{449}\! \left(x \right) = F_{450}\! \left(x \right)+F_{451}\! \left(x \right)
F_{450}\! \left(x \right) = F_{273}\! \left(x \right)
F_{451}\! \left(x \right) = F_{447}\! \left(x \right)
F_{452}\! \left(x \right) = F_{453}\! \left(x \right)
F_{453}\! \left(x \right) = F_{4}\! \left(x \right) F_{454}\! \left(x \right)
F_{454}\! \left(x \right) = F_{455}\! \left(x \right)+F_{456}\! \left(x \right)
F_{455}\! \left(x \right) = F_{443}\! \left(x \right)
F_{456}\! \left(x \right) = F_{457}\! \left(x \right)
F_{457}\! \left(x \right) = F_{4}\! \left(x \right) F_{458}\! \left(x \right)
F_{458}\! \left(x \right) = F_{459}\! \left(x \right)+F_{460}\! \left(x \right)
F_{459}\! \left(x \right) = F_{443}\! \left(x \right)
F_{460}\! \left(x \right) = F_{457}\! \left(x \right)
F_{461}\! \left(x \right) = F_{4}\! \left(x \right) F_{462}\! \left(x \right)
F_{462}\! \left(x \right) = F_{412}\! \left(x \right)
F_{463}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{464}\! \left(x \right)+F_{485}\! \left(x \right)
F_{464}\! \left(x \right) = F_{4}\! \left(x \right) F_{465}\! \left(x \right)
F_{465}\! \left(x \right) = F_{466}\! \left(x \right)+F_{470}\! \left(x \right)
F_{466}\! \left(x \right) = F_{369}\! \left(x \right)+F_{467}\! \left(x \right)
F_{467}\! \left(x \right) = F_{468}\! \left(x \right)
F_{468}\! \left(x \right) = F_{4}\! \left(x \right) F_{469}\! \left(x \right)
F_{469}\! \left(x \right) = F_{373}\! \left(x \right)
F_{470}\! \left(x \right) = F_{471}\! \left(x \right)+F_{476}\! \left(x \right)
F_{471}\! \left(x \right) = F_{472}\! \left(x \right)
F_{472}\! \left(x \right) = F_{4}\! \left(x \right) F_{473}\! \left(x \right)
F_{473}\! \left(x \right) = F_{474}\! \left(x \right)+F_{475}\! \left(x \right)
F_{474}\! \left(x \right) = F_{369}\! \left(x \right)
F_{475}\! \left(x \right) = F_{471}\! \left(x \right)
F_{476}\! \left(x \right) = F_{477}\! \left(x \right)
F_{477}\! \left(x \right) = F_{4}\! \left(x \right) F_{478}\! \left(x \right)
F_{478}\! \left(x \right) = F_{479}\! \left(x \right)+F_{480}\! \left(x \right)
F_{479}\! \left(x \right) = F_{467}\! \left(x \right)
F_{480}\! \left(x \right) = F_{481}\! \left(x \right)
F_{481}\! \left(x \right) = F_{4}\! \left(x \right) F_{482}\! \left(x \right)
F_{482}\! \left(x \right) = F_{483}\! \left(x \right)+F_{484}\! \left(x \right)
F_{483}\! \left(x \right) = F_{467}\! \left(x \right)
F_{484}\! \left(x \right) = F_{481}\! \left(x \right)
F_{485}\! \left(x \right) = F_{4}\! \left(x \right) F_{486}\! \left(x \right)
F_{486}\! \left(x \right) = F_{487}\! \left(x \right)+F_{488}\! \left(x \right)
F_{487}\! \left(x \right) = F_{412}\! \left(x \right)
F_{488}\! \left(x \right) = F_{439}\! \left(x \right)
F_{489}\! \left(x \right) = F_{4}\! \left(x \right) F_{490}\! \left(x \right)
F_{490}\! \left(x \right) = F_{491}\! \left(x \right)+F_{492}\! \left(x \right)
F_{491}\! \left(x \right) = F_{314}\! \left(x \right)+F_{412}\! \left(x \right)
F_{492}\! \left(x \right) = F_{341}\! \left(x \right)+F_{439}\! \left(x \right)
F_{493}\! \left(x \right) = F_{4}\! \left(x \right) F_{494}\! \left(x \right)
F_{494}\! \left(x \right) = F_{2}\! \left(x \right)+F_{314}\! \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_20(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))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_11(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_257(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_42(x))
Eq(F_25(x), F_26(x) + F_7(x))
Eq(F_26(x), F_22(x) + F_27(x) + F_37(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_33(x))
Eq(F_29(x), F_11(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_4(x))
Eq(F_33(x), F_17(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_30(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_14(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_4(x))
Eq(F_42(x), F_129(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_52(x))
Eq(F_46(x), F_47(x) + F_7(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_51(x))
Eq(F_50(x), F_11(x))
Eq(F_51(x), F_17(x))
Eq(F_52(x), F_43(x) + F_53(x))
Eq(F_53(x), 2*F_22(x) + F_54(x) + F_75(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_60(x))
Eq(F_56(x), F_47(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_51(x))
Eq(F_60(x), F_61(x) + F_66(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_47(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_57(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_57(x))
Eq(F_74(x), F_71(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_104(x) + F_77(x))
Eq(F_77(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_83(x))
Eq(F_81(x), F_11(x) + F_82(x))
Eq(F_82(x), F_48(x))
Eq(F_83(x), F_78(x) + F_84(x))
Eq(F_84(x), 2*F_22(x) + F_75(x) + F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_89(x))
Eq(F_87(x), F_82(x) + F_88(x))
Eq(F_88(x), F_58(x))
Eq(F_89(x), F_90(x) + F_95(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_82(x))
Eq(F_94(x), F_90(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_98(x) + F_99(x))
Eq(F_98(x), F_88(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_88(x))
Eq(F_103(x), F_100(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x) + F_127(x) + 2*F_22(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_108(x) + F_112(x))
Eq(F_108(x), F_109(x) + F_17(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_17(x))
Eq(F_112(x), F_113(x) + F_118(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_17(x))
Eq(F_117(x), F_113(x))
Eq(F_118(x), F_119(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_109(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_4(x))
Eq(F_124(x), F_125(x) + F_126(x))
Eq(F_125(x), F_109(x))
Eq(F_126(x), F_123(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_78(x))
Eq(F_129(x), F_130(x) + 2*F_22(x) + F_253(x))
Eq(F_130(x), F_131(x)*F_4(x))
Eq(F_131(x), F_132(x) + F_140(x))
Eq(F_132(x), F_133(x) + F_26(x))
Eq(F_133(x), F_134(x) + F_138(x) + 2*F_22(x))
Eq(F_134(x), F_135(x)*F_4(x))
Eq(F_135(x), F_136(x) + F_137(x))
Eq(F_136(x), F_30(x))
Eq(F_137(x), F_34(x))
Eq(F_138(x), F_139(x)*F_4(x))
Eq(F_139(x), F_33(x))
Eq(F_140(x), F_141(x) + F_227(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_143(x)*F_4(x))
Eq(F_143(x), F_144(x) + F_150(x))
Eq(F_144(x), F_145(x) + F_26(x))
Eq(F_145(x), F_146(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_30(x))
Eq(F_149(x), F_34(x))
Eq(F_150(x), F_141(x) + F_151(x))
Eq(F_151(x), F_152(x) + F_173(x) + 3*F_22(x))
Eq(F_152(x), F_153(x)*F_4(x))
Eq(F_153(x), F_154(x) + F_158(x))
Eq(F_154(x), F_145(x) + F_155(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_157(x)*F_4(x))
Eq(F_157(x), F_149(x))
Eq(F_158(x), F_159(x) + F_164(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_161(x)*F_4(x))
Eq(F_161(x), F_162(x) + F_163(x))
Eq(F_162(x), F_145(x))
Eq(F_163(x), F_159(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_166(x)*F_4(x))
Eq(F_166(x), F_167(x) + F_168(x))
Eq(F_167(x), F_155(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_170(x)*F_4(x))
Eq(F_170(x), F_171(x) + F_172(x))
Eq(F_171(x), F_155(x))
Eq(F_172(x), F_169(x))
Eq(F_173(x), F_174(x)*F_4(x))
Eq(F_174(x), F_175(x) + F_202(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_177(x))
Eq(F_177(x), F_178(x)*F_4(x))
Eq(F_178(x), F_179(x) + F_181(x))
Eq(F_179(x), F_180(x) + F_30(x))
Eq(F_180(x), F_146(x))
Eq(F_181(x), F_176(x) + F_182(x))
Eq(F_182(x), F_173(x) + F_183(x) + 3*F_22(x))
Eq(F_183(x), F_184(x)*F_4(x))
Eq(F_184(x), F_185(x) + F_187(x))
Eq(F_185(x), F_180(x) + F_186(x))
Eq(F_186(x), F_156(x))
Eq(F_187(x), F_188(x) + F_193(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_190(x)*F_4(x))
Eq(F_190(x), F_191(x) + F_192(x))
Eq(F_191(x), F_180(x))
Eq(F_192(x), F_188(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_195(x)*F_4(x))
Eq(F_195(x), F_196(x) + F_197(x))
Eq(F_196(x), F_186(x))
Eq(F_197(x), F_198(x))
Eq(F_198(x), F_199(x)*F_4(x))
Eq(F_199(x), F_200(x) + F_201(x))
Eq(F_200(x), F_186(x))
Eq(F_201(x), F_198(x))
Eq(F_202(x), F_203(x))
Eq(F_203(x), F_204(x) + 3*F_22(x) + F_225(x))
Eq(F_204(x), F_205(x)*F_4(x))
Eq(F_205(x), F_206(x) + F_210(x))
Eq(F_206(x), F_207(x) + F_34(x))
Eq(F_207(x), F_208(x))
Eq(F_208(x), F_209(x)*F_4(x))
Eq(F_209(x), F_34(x))
Eq(F_210(x), F_211(x) + F_216(x))
Eq(F_211(x), F_212(x))
Eq(F_212(x), F_213(x)*F_4(x))
Eq(F_213(x), F_214(x) + F_215(x))
Eq(F_214(x), F_34(x))
Eq(F_215(x), F_211(x))
Eq(F_216(x), F_217(x))
Eq(F_217(x), F_218(x)*F_4(x))
Eq(F_218(x), F_219(x) + F_220(x))
Eq(F_219(x), F_207(x))
Eq(F_220(x), F_221(x))
Eq(F_221(x), F_222(x)*F_4(x))
Eq(F_222(x), F_223(x) + F_224(x))
Eq(F_223(x), F_207(x))
Eq(F_224(x), F_221(x))
Eq(F_225(x), F_226(x)*F_4(x))
Eq(F_226(x), F_176(x))
Eq(F_227(x), 3*F_22(x) + F_228(x) + F_249(x))
Eq(F_228(x), F_229(x)*F_4(x))
Eq(F_229(x), F_230(x) + F_234(x))
Eq(F_230(x), F_133(x) + F_231(x))
Eq(F_231(x), F_232(x))
Eq(F_232(x), F_233(x)*F_4(x))
Eq(F_233(x), F_137(x))
Eq(F_234(x), F_235(x) + F_240(x))
Eq(F_235(x), F_236(x))
Eq(F_236(x), F_237(x)*F_4(x))
Eq(F_237(x), F_238(x) + F_239(x))
Eq(F_238(x), F_133(x))
Eq(F_239(x), F_235(x))
Eq(F_240(x), F_241(x))
Eq(F_241(x), F_242(x)*F_4(x))
Eq(F_242(x), F_243(x) + F_244(x))
Eq(F_243(x), F_231(x))
Eq(F_244(x), F_245(x))
Eq(F_245(x), F_246(x)*F_4(x))
Eq(F_246(x), F_247(x) + F_248(x))
Eq(F_247(x), F_231(x))
Eq(F_248(x), F_245(x))
Eq(F_249(x), F_250(x)*F_4(x))
Eq(F_250(x), F_251(x) + F_252(x))
Eq(F_251(x), F_176(x))
Eq(F_252(x), F_203(x))
Eq(F_253(x), F_254(x)*F_4(x))
Eq(F_254(x), F_255(x) + F_256(x))
Eq(F_255(x), F_176(x) + F_78(x))
Eq(F_256(x), F_105(x) + F_203(x))
Eq(F_257(x), F_258(x)*F_4(x))
Eq(F_258(x), F_259(x) + F_260(x))
Eq(F_259(x), F_2(x) + F_78(x))
Eq(F_260(x), F_105(x) + F_261(x))
Eq(F_261(x), F_22(x) + F_262(x) + F_493(x))
Eq(F_262(x), F_263(x)*F_4(x))
Eq(F_263(x), F_264(x) + F_278(x))
Eq(F_264(x), F_15(x) + F_265(x))
Eq(F_265(x), F_22(x) + F_266(x) + F_276(x))
Eq(F_266(x), F_267(x)*F_4(x))
Eq(F_267(x), F_268(x) + F_271(x))
Eq(F_268(x), F_269(x) + F_4(x))
Eq(F_269(x), F_270(x))
Eq(F_270(x), x**2)
Eq(F_271(x), F_272(x) + F_273(x))
Eq(F_272(x), F_40(x))
Eq(F_273(x), F_274(x))
Eq(F_274(x), F_275(x)*F_4(x))
Eq(F_275(x), F_269(x))
Eq(F_276(x), F_277(x)*F_4(x))
Eq(F_277(x), F_15(x) + F_272(x))
Eq(F_278(x), F_279(x) + F_365(x))
Eq(F_279(x), F_280(x))
Eq(F_280(x), F_281(x)*F_4(x))
Eq(F_281(x), F_282(x) + F_288(x))
Eq(F_282(x), F_15(x) + F_283(x))
Eq(F_283(x), F_284(x))
Eq(F_284(x), F_285(x)*F_4(x))
Eq(F_285(x), F_286(x) + F_287(x))
Eq(F_286(x), F_4(x))
Eq(F_287(x), F_272(x))
Eq(F_288(x), F_279(x) + F_289(x))
Eq(F_289(x), 2*F_22(x) + F_290(x) + F_311(x))
Eq(F_290(x), F_291(x)*F_4(x))
Eq(F_291(x), F_292(x) + F_296(x))
Eq(F_292(x), F_283(x) + F_293(x))
Eq(F_293(x), F_294(x))
Eq(F_294(x), F_295(x)*F_4(x))
Eq(F_295(x), F_287(x))
Eq(F_296(x), F_297(x) + F_302(x))
Eq(F_297(x), F_298(x))
Eq(F_298(x), F_299(x)*F_4(x))
Eq(F_299(x), F_300(x) + F_301(x))
Eq(F_300(x), F_283(x))
Eq(F_301(x), F_297(x))
Eq(F_302(x), F_303(x))
Eq(F_303(x), F_304(x)*F_4(x))
Eq(F_304(x), F_305(x) + F_306(x))
Eq(F_305(x), F_293(x))
Eq(F_306(x), F_307(x))
Eq(F_307(x), F_308(x)*F_4(x))
Eq(F_308(x), F_309(x) + F_310(x))
Eq(F_309(x), F_293(x))
Eq(F_310(x), F_307(x))
Eq(F_311(x), F_312(x)*F_4(x))
Eq(F_312(x), F_313(x) + F_340(x))
Eq(F_313(x), F_314(x))
Eq(F_314(x), F_315(x))
Eq(F_315(x), F_316(x)*F_4(x))
Eq(F_316(x), F_317(x) + F_319(x))
Eq(F_317(x), F_318(x) + F_4(x))
Eq(F_318(x), F_284(x))
Eq(F_319(x), F_314(x) + F_320(x))
Eq(F_320(x), 2*F_22(x) + F_311(x) + F_321(x))
Eq(F_321(x), F_322(x)*F_4(x))
Eq(F_322(x), F_323(x) + F_325(x))
Eq(F_323(x), F_318(x) + F_324(x))
Eq(F_324(x), F_294(x))
Eq(F_325(x), F_326(x) + F_331(x))
Eq(F_326(x), F_327(x))
Eq(F_327(x), F_328(x)*F_4(x))
Eq(F_328(x), F_329(x) + F_330(x))
Eq(F_329(x), F_318(x))
Eq(F_330(x), F_326(x))
Eq(F_331(x), F_332(x))
Eq(F_332(x), F_333(x)*F_4(x))
Eq(F_333(x), F_334(x) + F_335(x))
Eq(F_334(x), F_324(x))
Eq(F_335(x), F_336(x))
Eq(F_336(x), F_337(x)*F_4(x))
Eq(F_337(x), F_338(x) + F_339(x))
Eq(F_338(x), F_324(x))
Eq(F_339(x), F_336(x))
Eq(F_340(x), F_341(x))
Eq(F_341(x), 2*F_22(x) + F_342(x) + F_363(x))
Eq(F_342(x), F_343(x)*F_4(x))
Eq(F_343(x), F_344(x) + F_348(x))
Eq(F_344(x), F_272(x) + F_345(x))
Eq(F_345(x), F_346(x))
Eq(F_346(x), F_347(x)*F_4(x))
Eq(F_347(x), F_272(x))
Eq(F_348(x), F_349(x) + F_354(x))
Eq(F_349(x), F_350(x))
Eq(F_350(x), F_351(x)*F_4(x))
Eq(F_351(x), F_352(x) + F_353(x))
Eq(F_352(x), F_272(x))
Eq(F_353(x), F_349(x))
Eq(F_354(x), F_355(x))
Eq(F_355(x), F_356(x)*F_4(x))
Eq(F_356(x), F_357(x) + F_358(x))
Eq(F_357(x), F_345(x))
Eq(F_358(x), F_359(x))
Eq(F_359(x), F_360(x)*F_4(x))
Eq(F_360(x), F_361(x) + F_362(x))
Eq(F_361(x), F_345(x))
Eq(F_362(x), F_359(x))
Eq(F_363(x), F_364(x)*F_4(x))
Eq(F_364(x), F_314(x))
Eq(F_365(x), 2*F_22(x) + F_366(x) + F_489(x))
Eq(F_366(x), F_367(x)*F_4(x))
Eq(F_367(x), F_368(x) + F_376(x))
Eq(F_368(x), F_265(x) + F_369(x))
Eq(F_369(x), 2*F_22(x) + F_370(x) + F_374(x))
Eq(F_370(x), F_371(x)*F_4(x))
Eq(F_371(x), F_372(x) + F_373(x))
Eq(F_372(x), F_269(x))
Eq(F_373(x), F_273(x))
Eq(F_374(x), F_375(x)*F_4(x))
Eq(F_375(x), F_271(x))
Eq(F_376(x), F_377(x) + F_463(x))
Eq(F_377(x), F_378(x))
Eq(F_378(x), F_379(x)*F_4(x))
Eq(F_379(x), F_380(x) + F_386(x))
Eq(F_380(x), F_265(x) + F_381(x))
Eq(F_381(x), F_382(x))
Eq(F_382(x), F_383(x)*F_4(x))
Eq(F_383(x), F_384(x) + F_385(x))
Eq(F_384(x), F_269(x))
Eq(F_385(x), F_273(x))
Eq(F_386(x), F_377(x) + F_387(x))
Eq(F_387(x), 3*F_22(x) + F_388(x) + F_409(x))
Eq(F_388(x), F_389(x)*F_4(x))
Eq(F_389(x), F_390(x) + F_394(x))
Eq(F_390(x), F_381(x) + F_391(x))
Eq(F_391(x), F_392(x))
Eq(F_392(x), F_393(x)*F_4(x))
Eq(F_393(x), F_385(x))
Eq(F_394(x), F_395(x) + F_400(x))
Eq(F_395(x), F_396(x))
Eq(F_396(x), F_397(x)*F_4(x))
Eq(F_397(x), F_398(x) + F_399(x))
Eq(F_398(x), F_381(x))
Eq(F_399(x), F_395(x))
Eq(F_400(x), F_401(x))
Eq(F_401(x), F_4(x)*F_402(x))
Eq(F_402(x), F_403(x) + F_404(x))
Eq(F_403(x), F_391(x))
Eq(F_404(x), F_405(x))
Eq(F_405(x), F_4(x)*F_406(x))
Eq(F_406(x), F_407(x) + F_408(x))
Eq(F_407(x), F_391(x))
Eq(F_408(x), F_405(x))
Eq(F_409(x), F_4(x)*F_410(x))
Eq(F_410(x), F_411(x) + F_438(x))
Eq(F_411(x), F_412(x))
Eq(F_412(x), F_413(x))
Eq(F_413(x), F_4(x)*F_414(x))
Eq(F_414(x), F_415(x) + F_417(x))
Eq(F_415(x), F_269(x) + F_416(x))
Eq(F_416(x), F_382(x))
Eq(F_417(x), F_412(x) + F_418(x))
Eq(F_418(x), 3*F_22(x) + F_409(x) + F_419(x))
Eq(F_419(x), F_4(x)*F_420(x))
Eq(F_420(x), F_421(x) + F_423(x))
Eq(F_421(x), F_416(x) + F_422(x))
Eq(F_422(x), F_392(x))
Eq(F_423(x), F_424(x) + F_429(x))
Eq(F_424(x), F_425(x))
Eq(F_425(x), F_4(x)*F_426(x))
Eq(F_426(x), F_427(x) + F_428(x))
Eq(F_427(x), F_416(x))
Eq(F_428(x), F_424(x))
Eq(F_429(x), F_430(x))
Eq(F_430(x), F_4(x)*F_431(x))
Eq(F_431(x), F_432(x) + F_433(x))
Eq(F_432(x), F_422(x))
Eq(F_433(x), F_434(x))
Eq(F_434(x), F_4(x)*F_435(x))
Eq(F_435(x), F_436(x) + F_437(x))
Eq(F_436(x), F_422(x))
Eq(F_437(x), F_434(x))
Eq(F_438(x), F_439(x))
Eq(F_439(x), 3*F_22(x) + F_440(x) + F_461(x))
Eq(F_440(x), F_4(x)*F_441(x))
Eq(F_441(x), F_442(x) + F_446(x))
Eq(F_442(x), F_273(x) + F_443(x))
Eq(F_443(x), F_444(x))
Eq(F_444(x), F_4(x)*F_445(x))
Eq(F_445(x), F_273(x))
Eq(F_446(x), F_447(x) + F_452(x))
Eq(F_447(x), F_448(x))
Eq(F_448(x), F_4(x)*F_449(x))
Eq(F_449(x), F_450(x) + F_451(x))
Eq(F_450(x), F_273(x))
Eq(F_451(x), F_447(x))
Eq(F_452(x), F_453(x))
Eq(F_453(x), F_4(x)*F_454(x))
Eq(F_454(x), F_455(x) + F_456(x))
Eq(F_455(x), F_443(x))
Eq(F_456(x), F_457(x))
Eq(F_457(x), F_4(x)*F_458(x))
Eq(F_458(x), F_459(x) + F_460(x))
Eq(F_459(x), F_443(x))
Eq(F_460(x), F_457(x))
Eq(F_461(x), F_4(x)*F_462(x))
Eq(F_462(x), F_412(x))
Eq(F_463(x), 3*F_22(x) + F_464(x) + F_485(x))
Eq(F_464(x), F_4(x)*F_465(x))
Eq(F_465(x), F_466(x) + F_470(x))
Eq(F_466(x), F_369(x) + F_467(x))
Eq(F_467(x), F_468(x))
Eq(F_468(x), F_4(x)*F_469(x))
Eq(F_469(x), F_373(x))
Eq(F_470(x), F_471(x) + F_476(x))
Eq(F_471(x), F_472(x))
Eq(F_472(x), F_4(x)*F_473(x))
Eq(F_473(x), F_474(x) + F_475(x))
Eq(F_474(x), F_369(x))
Eq(F_475(x), F_471(x))
Eq(F_476(x), F_477(x))
Eq(F_477(x), F_4(x)*F_478(x))
Eq(F_478(x), F_479(x) + F_480(x))
Eq(F_479(x), F_467(x))
Eq(F_480(x), F_481(x))
Eq(F_481(x), F_4(x)*F_482(x))
Eq(F_482(x), F_483(x) + F_484(x))
Eq(F_483(x), F_467(x))
Eq(F_484(x), F_481(x))
Eq(F_485(x), F_4(x)*F_486(x))
Eq(F_486(x), F_487(x) + F_488(x))
Eq(F_487(x), F_412(x))
Eq(F_488(x), F_439(x))
Eq(F_489(x), F_4(x)*F_490(x))
Eq(F_490(x), F_491(x) + F_492(x))
Eq(F_491(x), F_314(x) + F_412(x))
Eq(F_492(x), F_341(x) + F_439(x))
Eq(F_493(x), F_4(x)*F_494(x))
Eq(F_494(x), F_2(x) + F_314(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:
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