0132_0213_2130_2310
Counting sequence:
1, 1, 2, 6, 20, 62, 166, 389, 822, 1609, 2982, 5328, 9320, 16176, 28174, 49679, 89194, 163459, 305646, 581746, 1123340, 2193138, 4316054, 8541353, 16966942, 33787949, 67393878, 134562916, 268850544, 537366756, 1074330494, 2148178515, 4295783122, 8590887623, 17180977246, 34361020966, 68720955156, 137440650886, 274879848518, 549758026893, 1099514141702, 2199026102225, 4398049724806, 8796096639800, 17592190105464, 35184376635736, 70368749255790, 140737494013143, 281474982999866, 562949960397003, 1125899914563406, 2251799822213402, 4503599636772124, 9007199265086170, 18014398520844918, 36028797031423153, 72057594051566318, 144115188090761013, 288230376167975990, 576460752321144140, 1152921504626126464, 2305843009234640012, 4611686018450113758, 9223372036879400347, 18446744073736199586, 36893488147447905423, 73786976294869299902, 147573952589709941070, 295147905179388938788, 590295810358744506350, 1180591620717453063718, 2361183241434867443989, 4722366482869693306326, 9444732965739341961817, 18889465931478636025190, 37778931862957220718240, 75557863725914386476680, 151115727451828714163840, 302231454903657365498062, 604462909807314663907487, 1208925819614629256239626, 2417851639229258436180499, 4835703278458516791092910, 9671406556917033495692994, 19342813113834066899403308, 38685626227668133701059010, 77371252455336267298320214, 154742504910672534486496697, 309485009821345068856197310, 618970019642690137588628797, 1237940039285380275046193430, 2475880078570760549953684276, 4951760157141521099760675728, 9903520314283042199366304564, 19807040628566084398568832062, 39614081257132168796964768227, 79228162514264337593747120242, 158456325028528675187301889367, 316912650057057350374401064734, 633825300114114700748588610934, 1267650600228229401496952443188
Generating function in Maple syntax:
-(4*x^7-3*x^6-17*x^5+31*x^4-33*x^3+21*x^2-7*x+1)/(2*x-1)/(x-1)^6
Generating function in latex syntax:
-\frac{4 x^{7}-3 x^{6}-17 x^{5}+31 x^{4}-33 x^{3}+21 x^{2}-7 x +1}{\left(2 x -1\right) \left(x -1\right)^{6}}
Generating function in sympy syntax:
(-4*x**7 + 3*x**6 + 17*x**5 - 31*x**4 + 33*x**3 - 21*x**2 + 7*x - 1)/((x - 1)**6*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x-1)^6*F(x)+4*x^7-3*x^6-17*x^5+31*x^4-33*x^3+21*x^2-7*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x -1\right)^{6} F \! \left(x \right)+4 x^{7}-3 x^{6}-17 x^{5}+31 x^{4}-33 x^{3}+21 x^{2}-7 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,2+2^n-157/30*n+3*n^2+1/40*n^5-19/24*n^3)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 2+2^{n}-\frac{157 n}{30}+3 n^{2}+\frac{n^{5}}{40}-\frac{19 n^{3}}{24} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 62
a(6) = 166
a(7) = 389
a(n+1) = 2*a(n)-1/120*(n-1)*(3*n^4-12*n^3-137*n^2+478*n-600), n >= 8
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) = 166
a \! \left(7\right) = 389
a \! \left(n +1\right) = 2 a \! \left(n \right)-\frac{\left(n -1\right) \left(3 n^{4}-12 n^{3}-137 n^{2}+478 n -600\right)}{120}, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15300/
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[12,x]*F[4,x]
F[4,x] = F[25,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[23,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[9,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[19,x]
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[1,x]+F[18,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[17,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[13,x]
F[25,x] = F[26,x]+F[40,x]
F[26,x] = F[27,x]
F[27,x] = F[12,x]*F[28,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[1,x]+F[14,x]
F[30,x] = F[18,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[17,x]+F[34,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[36,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[18,x]+F[35,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[34,x]
F[40,x] = F[113,x]+F[41,x]+F[42,x]
F[41,x] = 0
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[44,x]+F[60,x]
F[44,x] = F[45,x]+F[6,x]
F[45,x] = F[41,x]+F[46,x]+F[54,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[48,x]+F[51,x]
F[48,x] = F[10,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[12,x]*F[48,x]
F[51,x] = F[21,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[12,x]*F[51,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[13,x]+F[56,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[32,x]+F[41,x]+F[46,x]
F[58,x] = F[59,x]
F[59,x] = F[12,x]*F[56,x]
F[60,x] = F[61,x]+F[82,x]
F[61,x] = F[41,x]+F[62,x]+F[64,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[6,x]+F[61,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[66,x]+F[71,x]
F[66,x] = F[18,x]+F[67,x]
F[67,x] = F[41,x]+F[68,x]+F[70,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[10,x]+F[67,x]
F[70,x] = F[12,x]*F[66,x]
F[71,x] = F[72,x]+F[75,x]
F[72,x] = F[32,x]+F[41,x]+F[73,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[14,x]+F[31,x]
F[75,x] = 2*F[41,x]+F[76,x]+F[81,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[23,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[31,x]+F[78,x]
F[81,x] = F[12,x]*F[71,x]
F[82,x] = 2*F[41,x]+F[83,x]+F[94,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[85,x]+F[88,x]
F[85,x] = F[67,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[12,x]*F[85,x]
F[88,x] = F[89,x]+F[92,x]
F[89,x] = F[90,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[35,x]+F[89,x]
F[92,x] = F[93,x]
F[93,x] = F[12,x]*F[88,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = F[80,x]+F[96,x]
F[96,x] = F[111,x]+F[97,x]
F[97,x] = 2*F[41,x]+F[103,x]+F[98,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[100,x]+F[51,x]
F[100,x] = F[101,x]+F[38,x]
F[101,x] = F[102,x]
F[102,x] = F[100,x]*F[12,x]
F[103,x] = F[104,x]*F[12,x]
F[104,x] = F[105,x]+F[34,x]
F[105,x] = F[106,x]+F[109,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[12,x]
F[108,x] = F[106,x]+F[35,x]
F[109,x] = F[110,x]
F[110,x] = F[105,x]*F[12,x]
F[111,x] = F[112,x]
F[112,x] = F[12,x]*F[96,x]
F[113,x] = F[114,x]*F[12,x]
F[114,x] = F[115,x]+F[124,x]
F[115,x] = F[116,x]+F[26,x]
F[116,x] = F[117,x]+F[123,x]+F[41,x]
F[117,x] = F[118,x]*F[12,x]
F[118,x] = F[119,x]+F[121,x]
F[119,x] = F[10,x]+F[120,x]
F[120,x] = F[24,x]+F[41,x]+F[46,x]
F[121,x] = F[122,x]+F[67,x]
F[122,x] = 2*F[41,x]+F[79,x]+F[83,x]
F[123,x] = F[115,x]*F[12,x]
F[124,x] = F[125,x]+F[131,x]
F[125,x] = F[126,x]+F[32,x]+F[41,x]
F[126,x] = F[12,x]*F[127,x]
F[127,x] = F[128,x]+F[129,x]
F[128,x] = F[14,x]+F[57,x]
F[129,x] = F[130,x]+F[31,x]
F[130,x] = 2*F[41,x]+F[103,x]+F[98,x]
F[131,x] = 2*F[41,x]+F[132,x]+F[141,x]
F[132,x] = F[12,x]*F[133,x]
F[133,x] = F[134,x]+F[136,x]
F[134,x] = F[135,x]+F[23,x]
F[135,x] = F[59,x]
F[136,x] = F[137,x]+F[78,x]
F[137,x] = F[138,x]
F[138,x] = F[12,x]*F[139,x]
F[139,x] = F[130,x]+F[140,x]
F[140,x] = F[138,x]
F[141,x] = F[12,x]*F[124,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{25}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{23}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{40}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{30}\! \left(x \right) = F_{18}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \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_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{18}\! \left(x \right)+F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{40}\! \left(x \right) = F_{113}\! \left(x \right)+F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = 0
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{60}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{6}\! \left(x \right)
F_{45}\! \left(x \right) = F_{41}\! \left(x \right)+F_{46}\! \left(x \right)+F_{54}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{21}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{13}\! \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_{32}\! \left(x \right)+F_{41}\! \left(x \right)+F_{46}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{82}\! \left(x \right)
F_{61}\! \left(x \right) = F_{41}\! \left(x \right)+F_{62}\! \left(x \right)+F_{64}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{6}\! \left(x \right)+F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{71}\! \left(x \right)
F_{66}\! \left(x \right) = F_{18}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{41}\! \left(x \right)+F_{68}\! \left(x \right)+F_{70}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{10}\! \left(x \right)+F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = F_{32}\! \left(x \right)+F_{41}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{14}\! \left(x \right)+F_{31}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{41}\! \left(x \right)+F_{76}\! \left(x \right)+F_{81}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{23}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{31}\! \left(x \right)+F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{41}\! \left(x \right)+F_{83}\! \left(x \right)+F_{94}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{88}\! \left(x \right)
F_{85}\! \left(x \right) = F_{67}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{92}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{35}\! \left(x \right)+F_{89}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{80}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{111}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = 2 F_{41}\! \left(x \right)+F_{103}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{51}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{38}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{100}\! \left(x \right) F_{12}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{34}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{109}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{12}\! \left(x \right)
F_{108}\! \left(x \right) = F_{106}\! \left(x \right)+F_{35}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{12}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{124}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{26}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{123}\! \left(x \right)+F_{41}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{12}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{121}\! \left(x \right)
F_{119}\! \left(x \right) = F_{10}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{24}\! \left(x \right)+F_{41}\! \left(x \right)+F_{46}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{67}\! \left(x \right)
F_{122}\! \left(x \right) = 2 F_{41}\! \left(x \right)+F_{79}\! \left(x \right)+F_{83}\! \left(x \right)
F_{123}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{131}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{32}\! \left(x \right)+F_{41}\! \left(x \right)
F_{126}\! \left(x \right) = F_{12}\! \left(x \right) F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{129}\! \left(x \right)
F_{128}\! \left(x \right) = F_{14}\! \left(x \right)+F_{57}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{31}\! \left(x \right)
F_{130}\! \left(x \right) = 2 F_{41}\! \left(x \right)+F_{103}\! \left(x \right)+F_{98}\! \left(x \right)
F_{131}\! \left(x \right) = 2 F_{41}\! \left(x \right)+F_{132}\! \left(x \right)+F_{141}\! \left(x \right)
F_{132}\! \left(x \right) = F_{12}\! \left(x \right) F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{136}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{23}\! \left(x \right)
F_{135}\! \left(x \right) = F_{59}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{78}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{12}\! \left(x \right) F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{130}\! \left(x \right)+F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{138}\! \left(x \right)
F_{141}\! \left(x \right) = F_{12}\! \left(x \right) F_{124}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_25(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_23(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_9(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_1(x) + F_18(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_17(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_13(x))
Eq(F_25(x), F_26(x) + F_40(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_12(x)*F_28(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_1(x) + F_14(x))
Eq(F_30(x), F_18(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_17(x) + F_34(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_18(x) + F_35(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_34(x))
Eq(F_40(x), F_113(x) + F_41(x) + F_42(x))
Eq(F_41(x), 0)
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_60(x))
Eq(F_44(x), F_45(x) + F_6(x))
Eq(F_45(x), F_41(x) + F_46(x) + F_54(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_51(x))
Eq(F_48(x), F_10(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_12(x)*F_48(x))
Eq(F_51(x), F_21(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_12(x)*F_51(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_13(x) + F_56(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_32(x) + F_41(x) + F_46(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_12(x)*F_56(x))
Eq(F_60(x), F_61(x) + F_82(x))
Eq(F_61(x), F_41(x) + F_62(x) + F_64(x))
Eq(F_62(x), F_12(x)*F_63(x))
Eq(F_63(x), F_6(x) + F_61(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_71(x))
Eq(F_66(x), F_18(x) + F_67(x))
Eq(F_67(x), F_41(x) + F_68(x) + F_70(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_10(x) + F_67(x))
Eq(F_70(x), F_12(x)*F_66(x))
Eq(F_71(x), F_72(x) + F_75(x))
Eq(F_72(x), F_32(x) + F_41(x) + F_73(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_14(x) + F_31(x))
Eq(F_75(x), 2*F_41(x) + F_76(x) + F_81(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_23(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_31(x) + F_78(x))
Eq(F_81(x), F_12(x)*F_71(x))
Eq(F_82(x), 2*F_41(x) + F_83(x) + F_94(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_88(x))
Eq(F_85(x), F_67(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_12(x)*F_85(x))
Eq(F_88(x), F_89(x) + F_92(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_35(x) + F_89(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_12(x)*F_88(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_80(x) + F_96(x))
Eq(F_96(x), F_111(x) + F_97(x))
Eq(F_97(x), F_103(x) + 2*F_41(x) + F_98(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_51(x))
Eq(F_100(x), F_101(x) + F_38(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_100(x)*F_12(x))
Eq(F_103(x), F_104(x)*F_12(x))
Eq(F_104(x), F_105(x) + F_34(x))
Eq(F_105(x), F_106(x) + F_109(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_12(x))
Eq(F_108(x), F_106(x) + F_35(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_105(x)*F_12(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_12(x)*F_96(x))
Eq(F_113(x), F_114(x)*F_12(x))
Eq(F_114(x), F_115(x) + F_124(x))
Eq(F_115(x), F_116(x) + F_26(x))
Eq(F_116(x), F_117(x) + F_123(x) + F_41(x))
Eq(F_117(x), F_118(x)*F_12(x))
Eq(F_118(x), F_119(x) + F_121(x))
Eq(F_119(x), F_10(x) + F_120(x))
Eq(F_120(x), F_24(x) + F_41(x) + F_46(x))
Eq(F_121(x), F_122(x) + F_67(x))
Eq(F_122(x), 2*F_41(x) + F_79(x) + F_83(x))
Eq(F_123(x), F_115(x)*F_12(x))
Eq(F_124(x), F_125(x) + F_131(x))
Eq(F_125(x), F_126(x) + F_32(x) + F_41(x))
Eq(F_126(x), F_12(x)*F_127(x))
Eq(F_127(x), F_128(x) + F_129(x))
Eq(F_128(x), F_14(x) + F_57(x))
Eq(F_129(x), F_130(x) + F_31(x))
Eq(F_130(x), F_103(x) + 2*F_41(x) + F_98(x))
Eq(F_131(x), F_132(x) + F_141(x) + 2*F_41(x))
Eq(F_132(x), F_12(x)*F_133(x))
Eq(F_133(x), F_134(x) + F_136(x))
Eq(F_134(x), F_135(x) + F_23(x))
Eq(F_135(x), F_59(x))
Eq(F_136(x), F_137(x) + F_78(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_12(x)*F_139(x))
Eq(F_139(x), F_130(x) + F_140(x))
Eq(F_140(x), F_138(x))
Eq(F_141(x), F_12(x)*F_124(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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"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]]}]]}], "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], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], 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