0123_0213_1320_3021
Counting sequence:
1, 1, 2, 6, 20, 62, 174, 458, 1166, 2919, 7254, 17991, 44660, 111127, 277393, 694903, 1747416, 4411090, 11177969, 28431501, 72573505, 185864068, 477455691, 1229881398, 3175817379, 8218302152, 21306962474, 55330085938, 143879678971, 374580245239, 976152243814, 2545939175996, 6644717576920, 17352104598757, 45334816594788, 118489393418153, 309788137163046, 810144843718765, 2119104452360679, 5543917144879121, 14505800677842450, 37959087953522928, 99341226281712351, 260001162278658543, 680529356219156739, 1781308728534045242, 4662815185461945249, 12205921863830327168, 31952414926272793501, 83646036453466476134, 218974681710105154024, 573255086033260364276, 1500742901524765321405, 3928874539283330641437, 10285674958010618262908, 26927723337036318649478, 70496609532542437923426, 184560270043291138438115, 483180399558514605735714, 1264973060842521088660891, 3311722506958081898801320, 8670160809132212877433363, 22698690384855300670992461, 59425766734640666065573563, 155578313374111710549005724, 407308561762815051228815582, 1066346110618173067885862749, 2791727170253655708208098273, 7308830043669393762186239381, 19134751929601424053117495104, 50095403037192688322646474759, 131151410456373521423545407706, 343358732224390635798182576615, 898924588615274871486260686292, 2353414627497914838840043981878, 6161318459495339093064341623878, 16130539037359360746060316868431, 42230295134419706574321677754515, 110560339145401395613337781607074, 289450707487720805614825982771936, 757791752934055041503174811015740, 1983924489016985630044882092765873, 5193981586424112076058140141078896, 13598020008598468392676654885122333, 35600077903363807631945907987683834, 93202212603788309972076490810156297, 244006557660608023101296934839836099, 638817455778073014857758022495355253, 1672445800260914588592691103104602486, 4378519925748900293898326235364058524, 11463113937603818789776168775747431019, 30010821806538425076778825634305197411, 78569351317404116832512306478421629175, 205697231809263719729875776487627324822, 538522343423020835519507304516475080573, 1409869797055665297229723011817726908228, 3691087044876286955101197454862901138561, 9663391331717739182150659234788399107090, 25299086938323381571843906028096652516884, 66233869458855083238874180687100201289256, 173402521388456871524439936906191657617585
Generating function in Maple syntax:
(8*x^16-44*x^15+65*x^14+34*x^13-172*x^12+112*x^11+146*x^10-315*x^9+172*x^8+278*x^7-769*x^6+918*x^5-661*x^4+302*x^3-86*x^2+14*x-1)/(x^2-3*x+1)/(x^2+x-1)/(2*x-1)^3/(x-1)^5
Generating function in latex syntax:
\frac{8 x^{16}-44 x^{15}+65 x^{14}+34 x^{13}-172 x^{12}+112 x^{11}+146 x^{10}-315 x^{9}+172 x^{8}+278 x^{7}-769 x^{6}+918 x^{5}-661 x^{4}+302 x^{3}-86 x^{2}+14 x -1}{\left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(2 x -1\right)^{3} \left(x -1\right)^{5}}
Generating function in sympy syntax:
(8*x**16 - 44*x**15 + 65*x**14 + 34*x**13 - 172*x**12 + 112*x**11 + 146*x**10 - 315*x**9 + 172*x**8 + 278*x**7 - 769*x**6 + 918*x**5 - 661*x**4 + 302*x**3 - 86*x**2 + 14*x - 1)/((x - 1)**5*(2*x - 1)**3*(x**2 - 3*x + 1)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)*(x^2+x-1)*(2*x-1)^3*(x-1)^5*F(x)+8*x^16-44*x^15+65*x^14+34*x^13-172*x^12+112*x^11+146*x^10-315*x^9+172*x^8+278*x^7-769*x^6+918*x^5-661*x^4+302*x^3-86*x^2+14*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(2 x -1\right)^{3} \left(x -1\right)^{5} F \! \left(x \right)+8 x^{16}-44 x^{15}+65 x^{14}+34 x^{13}-172 x^{12}+112 x^{11}+146 x^{10}-315 x^{9}+172 x^{8}+278 x^{7}-769 x^{6}+918 x^{5}-661 x^{4}+302 x^{3}-86 x^{2}+14 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,131/16,n = 1,113/16,n = 2,43/8,n = 3,3,n = 4,1,0)+1/960*(-96*5^(1/2)+480)*(3/2-1/2*5^(1/2))^(-n)+1/960*(96*5^(1/2)+480)*(3/2+1/2*5^(1/2))^(-n)+1/960*(-288*5^(1/2)+480)*(-1/2*5^(1/2)-1/2)^(-n)+1/960*(288*5^(1/2)+480)*(1/2*5^(1/2)-1/2)^(-n)+1/960*(15*n^2+135*n-180)*2^n+1/24*n^4-5/12*n^3+23/24*n^2-7/12*n-9
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}\frac{131}{16} & n =0 \\ \frac{113}{16} & n =1 \\ \frac{43}{8} & n =2 \\ 3 & n =3 \\ 1 & n =4 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{\left(-96 \sqrt{5}+480\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{960}+\frac{\left(96 \sqrt{5}+480\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{960}+\frac{\left(-288 \sqrt{5}+480\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{960}+\frac{\left(288 \sqrt{5}+480\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{960}+\frac{\left(15 n^{2}+135 n -180\right) 2^{n}}{960}+\frac{n^{4}}{24}-\frac{5 n^{3}}{12}+\frac{23 n^{2}}{24}-\frac{7 n}{12}-9
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 62
a(6) = 174
a(7) = 458
a(8) = 1166
a(9) = 2919
a(10) = 7254
a(11) = 17991
a(12) = 44660
a(13) = 111127
a(14) = 277393
a(15) = 694903
a(16) = 1747416
a(n+7) = -1/24*n^4+11/12*n^3-95/24*n^2-8*a(n)+28*a(n+1)-6*a(n+2)-55*a(n+3)+72*a(n+4)-39*a(n+5)+10*a(n+6)-59/12*n+25, n >= 17
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 62
a \! \left(6\right) = 174
a \! \left(7\right) = 458
a \! \left(8\right) = 1166
a \! \left(9\right) = 2919
a \! \left(10\right) = 7254
a \! \left(11\right) = 17991
a \! \left(12\right) = 44660
a \! \left(13\right) = 111127
a \! \left(14\right) = 277393
a \! \left(15\right) = 694903
a \! \left(16\right) = 1747416
a \! \left(n +7\right) = -\frac{n^{4}}{24}+\frac{11 n^{3}}{12}-\frac{95 n^{2}}{24}-8 a \! \left(n \right)+28 a \! \left(n +1\right)-6 a \! \left(n +2\right)-55 a \! \left(n +3\right)+72 a \! \left(n +4\right)-39 a \! \left(n +5\right)+10 a \! \left(n +6\right)-\frac{59 n}{12}+25, \quad n \geq 17
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14941/
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[24,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[21,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[4,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[14,x]*F[4,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[14,x]
F[24,x] = F[25,x]+F[62,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[1,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[17,x]*F[4,x]
F[31,x] = F[25,x]+F[32,x]
F[32,x] = F[33,x]+F[34,x]+F[60,x]
F[33,x] = 0
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[40,x]
F[36,x] = F[29,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[4,x]
F[40,x] = F[32,x]+F[41,x]
F[41,x] = 2*F[33,x]+F[42,x]+F[46,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[37,x]
F[45,x] = F[41,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[33,x]+F[49,x]+F[59,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[53,x]
F[51,x] = F[4,x]+F[52,x]
F[52,x] = F[38,x]
F[53,x] = F[48,x]+F[54,x]
F[54,x] = 2*F[33,x]+F[46,x]+F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[52,x]
F[58,x] = F[54,x]
F[59,x] = F[25,x]*F[4,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[25,x]+F[48,x]
F[62,x] = F[224,x]+F[33,x]+F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]+F[83,x]
F[65,x] = F[66,x]+F[7,x]
F[66,x] = F[33,x]+F[67,x]+F[72,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[11,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[4,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[78,x]
F[74,x] = F[29,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[29,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[38,x]
F[80,x] = F[81,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[79,x]
F[83,x] = F[62,x]+F[84,x]
F[84,x] = F[149,x]+F[189,x]+F[33,x]+F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[87,x]+F[97,x]
F[87,x] = F[66,x]+F[88,x]
F[88,x] = 2*F[33,x]+F[89,x]+F[91,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[69,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[37,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[37,x]
F[97,x] = F[84,x]+F[98,x]
F[98,x] = 2*F[33,x]+F[103,x]+F[135,x]+F[99,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[88,x]
F[102,x] = F[98,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]
F[105,x] = 2*F[33,x]+F[106,x]+F[123,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[69,x]
F[109,x] = 2*F[33,x]+F[110,x]+F[89,x]
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[52,x]
F[112,x] = F[105,x]+F[113,x]
F[113,x] = 2*F[33,x]+F[103,x]+F[114,x]+F[118,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[116,x]+F[117,x]
F[116,x] = F[109,x]
F[117,x] = F[113,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[57,x]
F[122,x] = F[120,x]
F[123,x] = F[124,x]*F[4,x]
F[124,x] = F[125,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[4,x]
F[127,x] = F[128,x]+F[51,x]
F[128,x] = F[125,x]+F[129,x]
F[129,x] = 2*F[33,x]+F[130,x]+F[133,x]
F[130,x] = F[131,x]*F[4,x]
F[131,x] = F[132,x]+F[57,x]
F[132,x] = F[129,x]
F[133,x] = F[134,x]*F[4,x]
F[134,x] = F[125,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[137,x]
F[137,x] = F[138,x]+F[142,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]*F[4,x]
F[140,x] = F[141,x]+F[44,x]
F[141,x] = F[138,x]
F[142,x] = 3*F[33,x]+F[143,x]+F[147,x]
F[143,x] = F[144,x]*F[4,x]
F[144,x] = F[145,x]+F[146,x]
F[145,x] = F[94,x]
F[146,x] = F[142,x]
F[147,x] = F[148,x]*F[4,x]
F[148,x] = F[138,x]
F[149,x] = F[150,x]*F[4,x]
F[150,x] = F[105,x]+F[151,x]
F[151,x] = F[152,x]+F[186,x]+F[33,x]
F[152,x] = F[153,x]*F[4,x]
F[153,x] = F[154,x]+F[159,x]
F[154,x] = F[11,x]+F[155,x]
F[155,x] = F[156,x]+F[33,x]+F[67,x]
F[156,x] = F[157,x]*F[4,x]
F[157,x] = F[158,x]+F[29,x]
F[158,x] = F[38,x]
F[159,x] = F[151,x]+F[160,x]
F[160,x] = F[149,x]+F[161,x]+F[175,x]+F[33,x]
F[161,x] = F[162,x]*F[4,x]
F[162,x] = F[163,x]+F[167,x]
F[163,x] = F[155,x]+F[164,x]
F[164,x] = 2*F[33,x]+F[165,x]+F[89,x]
F[165,x] = F[166,x]*F[4,x]
F[166,x] = F[37,x]
F[167,x] = F[160,x]+F[168,x]
F[168,x] = 2*F[33,x]+F[103,x]+F[169,x]+F[173,x]
F[169,x] = F[170,x]*F[4,x]
F[170,x] = F[171,x]+F[172,x]
F[171,x] = F[164,x]
F[172,x] = F[168,x]
F[173,x] = F[174,x]*F[4,x]
F[174,x] = F[138,x]
F[175,x] = F[176,x]*F[4,x]
F[176,x] = F[177,x]+F[185,x]
F[177,x] = F[178,x]
F[178,x] = F[179,x]*F[4,x]
F[179,x] = F[180,x]+F[36,x]
F[180,x] = F[177,x]+F[181,x]
F[181,x] = 2*F[33,x]+F[133,x]+F[182,x]
F[182,x] = F[183,x]*F[4,x]
F[183,x] = F[184,x]+F[44,x]
F[184,x] = F[181,x]
F[185,x] = F[120,x]
F[186,x] = F[187,x]*F[4,x]
F[187,x] = F[188,x]+F[25,x]
F[188,x] = F[126,x]
F[189,x] = F[190,x]*F[4,x]
F[190,x] = F[191,x]+F[219,x]
F[191,x] = F[177,x]+F[192,x]
F[192,x] = 2*F[33,x]+F[193,x]+F[217,x]
F[193,x] = F[194,x]*F[4,x]
F[194,x] = F[195,x]+F[199,x]
F[195,x] = F[196,x]+F[75,x]
F[196,x] = 2*F[33,x]+F[197,x]+F[89,x]
F[197,x] = F[198,x]*F[4,x]
F[198,x] = F[37,x]
F[199,x] = F[192,x]+F[200,x]
F[200,x] = 2*F[33,x]+F[201,x]+F[205,x]+F[215,x]
F[201,x] = F[202,x]*F[4,x]
F[202,x] = F[203,x]+F[204,x]
F[203,x] = F[196,x]
F[204,x] = F[200,x]
F[205,x] = F[206,x]*F[4,x]
F[206,x] = F[207,x]
F[207,x] = 2*F[33,x]+F[123,x]+F[208,x]
F[208,x] = F[209,x]*F[4,x]
F[209,x] = F[108,x]+F[210,x]
F[210,x] = F[207,x]+F[211,x]
F[211,x] = 2*F[33,x]+F[118,x]+F[205,x]+F[212,x]
F[212,x] = F[213,x]*F[4,x]
F[213,x] = F[116,x]+F[214,x]
F[214,x] = F[211,x]
F[215,x] = F[216,x]*F[4,x]
F[216,x] = F[138,x]
F[217,x] = F[218,x]*F[4,x]
F[218,x] = F[177,x]
F[219,x] = F[220,x]+F[221,x]
F[220,x] = F[139,x]
F[221,x] = 3*F[33,x]+F[143,x]+F[222,x]
F[222,x] = F[223,x]*F[4,x]
F[223,x] = F[220,x]
F[224,x] = F[225,x]*F[4,x]
F[225,x] = F[226,x]+F[227,x]
F[226,x] = F[151,x]+F[25,x]
F[227,x] = F[228,x]+F[229,x]
F[228,x] = F[178,x]
F[229,x] = 2*F[33,x]+F[193,x]+F[230,x]
F[230,x] = F[231,x]*F[4,x]
F[231,x] = F[228,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_{24}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{62}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{60}\! \left(x \right)
F_{33}\! \left(x \right) = 0
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{36}\! \left(x \right) = F_{29}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = F_{32}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{42}\! \left(x \right)+F_{46}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{37}\! \left(x \right)
F_{45}\! \left(x \right) = F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{33}\! \left(x \right)+F_{49}\! \left(x \right)+F_{59}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{38}\! \left(x \right)
F_{53}\! \left(x \right) = F_{48}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{46}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{52}\! \left(x \right)
F_{58}\! \left(x \right) = F_{54}\! \left(x \right)
F_{59}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{25}\! \left(x \right)+F_{48}\! \left(x \right)
F_{62}\! \left(x \right) = F_{224}\! \left(x \right)+F_{33}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{83}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{7}\! \left(x \right)
F_{66}\! \left(x \right) = F_{33}\! \left(x \right)+F_{67}\! \left(x \right)+F_{72}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{78}\! \left(x \right)
F_{74}\! \left(x \right) = F_{29}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{29}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{38}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{79}\! \left(x \right)
F_{83}\! \left(x \right) = F_{62}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{149}\! \left(x \right)+F_{189}\! \left(x \right)+F_{33}\! \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_{97}\! \left(x \right)
F_{87}\! \left(x \right) = F_{66}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{89}\! \left(x \right)+F_{91}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{69}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{37}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{37}\! \left(x \right)
F_{97}\! \left(x \right) = F_{84}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{103}\! \left(x \right)+F_{135}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{88}\! \left(x \right)
F_{102}\! \left(x \right) = F_{98}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{106}\! \left(x \right)+F_{123}\! \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_{69}\! \left(x \right)
F_{109}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{110}\! \left(x \right)+F_{89}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{52}\! \left(x \right)
F_{112}\! \left(x \right) = F_{105}\! \left(x \right)+F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{103}\! \left(x \right)+F_{114}\! \left(x \right)+F_{118}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{117}\! \left(x \right)
F_{116}\! \left(x \right) = F_{109}\! \left(x \right)
F_{117}\! \left(x \right) = F_{113}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{57}\! \left(x \right)
F_{122}\! \left(x \right) = F_{120}\! \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_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{4}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{51}\! \left(x \right)
F_{128}\! \left(x \right) = F_{125}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{130}\! \left(x \right)+F_{133}\! \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_{57}\! \left(x \right)
F_{132}\! \left(x \right) = F_{129}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = F_{125}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{142}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{44}\! \left(x \right)
F_{141}\! \left(x \right) = F_{138}\! \left(x \right)
F_{142}\! \left(x \right) = 3 F_{33}\! \left(x \right)+F_{143}\! \left(x \right)+F_{147}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{4}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{146}\! \left(x \right)
F_{145}\! \left(x \right) = F_{94}\! \left(x \right)
F_{146}\! \left(x \right) = F_{142}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{4}\! \left(x \right)
F_{148}\! \left(x \right) = F_{138}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{4}\! \left(x \right)
F_{150}\! \left(x \right) = F_{105}\! \left(x \right)+F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{186}\! \left(x \right)+F_{33}\! \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_{159}\! \left(x \right)
F_{154}\! \left(x \right) = F_{11}\! \left(x \right)+F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{33}\! \left(x \right)+F_{67}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right) F_{4}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{29}\! \left(x \right)
F_{158}\! \left(x \right) = F_{38}\! \left(x \right)
F_{159}\! \left(x \right) = F_{151}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{149}\! \left(x \right)+F_{161}\! \left(x \right)+F_{175}\! \left(x \right)+F_{33}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right) F_{4}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{167}\! \left(x \right)
F_{163}\! \left(x \right) = F_{155}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{165}\! \left(x \right)+F_{89}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{4}\! \left(x \right)
F_{166}\! \left(x \right) = F_{37}\! \left(x \right)
F_{167}\! \left(x \right) = F_{160}\! \left(x \right)+F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{103}\! \left(x \right)+F_{169}\! \left(x \right)+F_{173}\! \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_{164}\! \left(x \right)
F_{172}\! \left(x \right) = F_{168}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right) F_{4}\! \left(x \right)
F_{174}\! \left(x \right) = F_{138}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right) F_{4}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{185}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right) F_{4}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{36}\! \left(x \right)
F_{180}\! \left(x \right) = F_{177}\! \left(x \right)+F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{133}\! \left(x \right)+F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right) F_{4}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{44}\! \left(x \right)
F_{184}\! \left(x \right) = F_{181}\! \left(x \right)
F_{185}\! \left(x \right) = F_{120}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right) F_{4}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{25}\! \left(x \right)
F_{188}\! \left(x \right) = F_{126}\! \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_{219}\! \left(x \right)
F_{191}\! \left(x \right) = F_{177}\! \left(x \right)+F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{193}\! \left(x \right)+F_{217}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right) F_{4}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)+F_{199}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)+F_{75}\! \left(x \right)
F_{196}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{197}\! \left(x \right)+F_{89}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right) F_{4}\! \left(x \right)
F_{198}\! \left(x \right) = F_{37}\! \left(x \right)
F_{199}\! \left(x \right) = F_{192}\! \left(x \right)+F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{201}\! \left(x \right)+F_{205}\! \left(x \right)+F_{215}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right) F_{4}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)+F_{204}\! \left(x \right)
F_{203}\! \left(x \right) = F_{196}\! \left(x \right)
F_{204}\! \left(x \right) = F_{200}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right) F_{4}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{123}\! \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_{108}\! \left(x \right)+F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = F_{207}\! \left(x \right)+F_{211}\! \left(x \right)
F_{211}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{118}\! \left(x \right)+F_{205}\! \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_{116}\! \left(x \right)+F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = F_{211}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right) F_{4}\! \left(x \right)
F_{216}\! \left(x \right) = F_{138}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right) F_{4}\! \left(x \right)
F_{218}\! \left(x \right) = F_{177}\! \left(x \right)
F_{219}\! \left(x \right) = F_{220}\! \left(x \right)+F_{221}\! \left(x \right)
F_{220}\! \left(x \right) = F_{139}\! \left(x \right)
F_{221}\! \left(x \right) = 3 F_{33}\! \left(x \right)+F_{143}\! \left(x \right)+F_{222}\! \left(x \right)
F_{222}\! \left(x \right) = F_{223}\! \left(x \right) F_{4}\! \left(x \right)
F_{223}\! \left(x \right) = F_{220}\! \left(x \right)
F_{224}\! \left(x \right) = F_{225}\! \left(x \right) F_{4}\! \left(x \right)
F_{225}\! \left(x \right) = F_{226}\! \left(x \right)+F_{227}\! \left(x \right)
F_{226}\! \left(x \right) = F_{151}\! \left(x \right)+F_{25}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)+F_{229}\! \left(x \right)
F_{228}\! \left(x \right) = F_{178}\! \left(x \right)
F_{229}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{193}\! \left(x \right)+F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right) F_{4}\! \left(x \right)
F_{231}\! \left(x \right) = F_{228}\! \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_24(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_21(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_4(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_14(x)*F_4(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_14(x))
Eq(F_24(x), F_25(x) + F_62(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_1(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_17(x)*F_4(x))
Eq(F_31(x), F_25(x) + F_32(x))
Eq(F_32(x), F_33(x) + F_34(x) + F_60(x))
Eq(F_33(x), 0)
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_40(x))
Eq(F_36(x), F_29(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_4(x))
Eq(F_40(x), F_32(x) + F_41(x))
Eq(F_41(x), 2*F_33(x) + F_42(x) + F_46(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_37(x))
Eq(F_45(x), F_41(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_33(x) + F_49(x) + F_59(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_53(x))
Eq(F_51(x), F_4(x) + F_52(x))
Eq(F_52(x), F_38(x))
Eq(F_53(x), F_48(x) + F_54(x))
Eq(F_54(x), 2*F_33(x) + F_46(x) + F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_52(x))
Eq(F_58(x), F_54(x))
Eq(F_59(x), F_25(x)*F_4(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_25(x) + F_48(x))
Eq(F_62(x), F_224(x) + F_33(x) + F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_83(x))
Eq(F_65(x), F_66(x) + F_7(x))
Eq(F_66(x), F_33(x) + F_67(x) + F_72(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_11(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_4(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_78(x))
Eq(F_74(x), F_29(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_29(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_38(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_79(x))
Eq(F_83(x), F_62(x) + F_84(x))
Eq(F_84(x), F_149(x) + F_189(x) + F_33(x) + F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_97(x))
Eq(F_87(x), F_66(x) + F_88(x))
Eq(F_88(x), 2*F_33(x) + F_89(x) + F_91(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_69(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_37(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_37(x))
Eq(F_97(x), F_84(x) + F_98(x))
Eq(F_98(x), F_103(x) + F_135(x) + 2*F_33(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_88(x))
Eq(F_102(x), F_98(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x) + F_123(x) + 2*F_33(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_69(x))
Eq(F_109(x), F_110(x) + 2*F_33(x) + F_89(x))
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_52(x))
Eq(F_112(x), F_105(x) + F_113(x))
Eq(F_113(x), F_103(x) + F_114(x) + F_118(x) + 2*F_33(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_109(x))
Eq(F_117(x), F_113(x))
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_57(x))
Eq(F_122(x), F_120(x))
Eq(F_123(x), F_124(x)*F_4(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_4(x))
Eq(F_127(x), F_128(x) + F_51(x))
Eq(F_128(x), F_125(x) + F_129(x))
Eq(F_129(x), F_130(x) + F_133(x) + 2*F_33(x))
Eq(F_130(x), F_131(x)*F_4(x))
Eq(F_131(x), F_132(x) + F_57(x))
Eq(F_132(x), F_129(x))
Eq(F_133(x), F_134(x)*F_4(x))
Eq(F_134(x), F_125(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_138(x) + F_142(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x)*F_4(x))
Eq(F_140(x), F_141(x) + F_44(x))
Eq(F_141(x), F_138(x))
Eq(F_142(x), F_143(x) + F_147(x) + 3*F_33(x))
Eq(F_143(x), F_144(x)*F_4(x))
Eq(F_144(x), F_145(x) + F_146(x))
Eq(F_145(x), F_94(x))
Eq(F_146(x), F_142(x))
Eq(F_147(x), F_148(x)*F_4(x))
Eq(F_148(x), F_138(x))
Eq(F_149(x), F_150(x)*F_4(x))
Eq(F_150(x), F_105(x) + F_151(x))
Eq(F_151(x), F_152(x) + F_186(x) + F_33(x))
Eq(F_152(x), F_153(x)*F_4(x))
Eq(F_153(x), F_154(x) + F_159(x))
Eq(F_154(x), F_11(x) + F_155(x))
Eq(F_155(x), F_156(x) + F_33(x) + F_67(x))
Eq(F_156(x), F_157(x)*F_4(x))
Eq(F_157(x), F_158(x) + F_29(x))
Eq(F_158(x), F_38(x))
Eq(F_159(x), F_151(x) + F_160(x))
Eq(F_160(x), F_149(x) + F_161(x) + F_175(x) + F_33(x))
Eq(F_161(x), F_162(x)*F_4(x))
Eq(F_162(x), F_163(x) + F_167(x))
Eq(F_163(x), F_155(x) + F_164(x))
Eq(F_164(x), F_165(x) + 2*F_33(x) + F_89(x))
Eq(F_165(x), F_166(x)*F_4(x))
Eq(F_166(x), F_37(x))
Eq(F_167(x), F_160(x) + F_168(x))
Eq(F_168(x), F_103(x) + F_169(x) + F_173(x) + 2*F_33(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_164(x))
Eq(F_172(x), F_168(x))
Eq(F_173(x), F_174(x)*F_4(x))
Eq(F_174(x), F_138(x))
Eq(F_175(x), F_176(x)*F_4(x))
Eq(F_176(x), F_177(x) + F_185(x))
Eq(F_177(x), F_178(x))
Eq(F_178(x), F_179(x)*F_4(x))
Eq(F_179(x), F_180(x) + F_36(x))
Eq(F_180(x), F_177(x) + F_181(x))
Eq(F_181(x), F_133(x) + F_182(x) + 2*F_33(x))
Eq(F_182(x), F_183(x)*F_4(x))
Eq(F_183(x), F_184(x) + F_44(x))
Eq(F_184(x), F_181(x))
Eq(F_185(x), F_120(x))
Eq(F_186(x), F_187(x)*F_4(x))
Eq(F_187(x), F_188(x) + F_25(x))
Eq(F_188(x), F_126(x))
Eq(F_189(x), F_190(x)*F_4(x))
Eq(F_190(x), F_191(x) + F_219(x))
Eq(F_191(x), F_177(x) + F_192(x))
Eq(F_192(x), F_193(x) + F_217(x) + 2*F_33(x))
Eq(F_193(x), F_194(x)*F_4(x))
Eq(F_194(x), F_195(x) + F_199(x))
Eq(F_195(x), F_196(x) + F_75(x))
Eq(F_196(x), F_197(x) + 2*F_33(x) + F_89(x))
Eq(F_197(x), F_198(x)*F_4(x))
Eq(F_198(x), F_37(x))
Eq(F_199(x), F_192(x) + F_200(x))
Eq(F_200(x), F_201(x) + F_205(x) + F_215(x) + 2*F_33(x))
Eq(F_201(x), F_202(x)*F_4(x))
Eq(F_202(x), F_203(x) + F_204(x))
Eq(F_203(x), F_196(x))
Eq(F_204(x), F_200(x))
Eq(F_205(x), F_206(x)*F_4(x))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_123(x) + F_208(x) + 2*F_33(x))
Eq(F_208(x), F_209(x)*F_4(x))
Eq(F_209(x), F_108(x) + F_210(x))
Eq(F_210(x), F_207(x) + F_211(x))
Eq(F_211(x), F_118(x) + F_205(x) + F_212(x) + 2*F_33(x))
Eq(F_212(x), F_213(x)*F_4(x))
Eq(F_213(x), F_116(x) + F_214(x))
Eq(F_214(x), F_211(x))
Eq(F_215(x), F_216(x)*F_4(x))
Eq(F_216(x), F_138(x))
Eq(F_217(x), F_218(x)*F_4(x))
Eq(F_218(x), F_177(x))
Eq(F_219(x), F_220(x) + F_221(x))
Eq(F_220(x), F_139(x))
Eq(F_221(x), F_143(x) + F_222(x) + 3*F_33(x))
Eq(F_222(x), F_223(x)*F_4(x))
Eq(F_223(x), F_220(x))
Eq(F_224(x), F_225(x)*F_4(x))
Eq(F_225(x), F_226(x) + F_227(x))
Eq(F_226(x), F_151(x) + F_25(x))
Eq(F_227(x), F_228(x) + F_229(x))
Eq(F_228(x), F_178(x))
Eq(F_229(x), F_193(x) + F_230(x) + 2*F_33(x))
Eq(F_230(x), F_231(x)*F_4(x))
Eq(F_231(x), F_228(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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": 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