0132_0213_0231_1302_2310
Counting sequence:
1, 1, 2, 6, 19, 54, 136, 314, 687, 1460, 3064, 6412, 13443, 28274, 59632, 125974, 266239, 562376, 1186448, 2498936, 5253539, 11023158, 23084632, 48253746, 100686319, 209742524, 436239816, 906007364, 1879092067, 3892364890, 8053122144, 16643065262, 34359814783, 70867047184, 146028986272, 300647821424, 618475414979, 1271310458846, 2611340271368, 5360119358346, 10995116469679, 22539988581828, 46179488601112, 94558000247036, 193514046772419, 395824186310594, 809240558383696, 1653665488547014, 3377699720933247, 6896136929852120, 14073748836011824, 28710447625006312, 58546795156378723, 119345390125925894, 243194379878662712, 495395959011461474, 1008806316531751919, 2053641430081763916, 4179340454200698088, 8502796096476437556, 17293822569103712419, 35164105890509910698, 71481133285625664192, 145268109580463948126, 295147905179354136319, 599519182395561823264, 1217485108864831891776, 2471863705877081495264, 5017514388048999716227, 10182602728687674271150, 20660353362554699696104, 41911002535468103269562, 85002596691653615961263, 172366376624742052536404, 349455119732353748176952, 708354972430446784550124, 1435599410792372147597059, 2908977753447701454413586, 5893513370621317229618608, 11938142468694463103304566, 24178516392292583497365759, 48961495694392481579009768, 99131917208399592329489872, 200681686056028443004989016, 406199075390515402705226019, 822069557337947838804344534, 1663481927789729744400044056, 3365649481807127622386548114, 6808670216069591511949953007, 13772082937049855558257749980, 27853650883921056185235518984, 56326271787484802507915615012, 113890483614254985290725138403, 230256847307080731131243070714, 465465454771302983362076936992, 940834429856889008923340911374, 1901475900342344102245061590399, 3842565881941820373286888663856, 7764359926397905084167314504928, 15687176177824338843521709847376, 31691265005705735037417588133699
Generating function in Maple syntax:
(2*x^8-4*x^7-9*x^6+29*x^5-48*x^4+48*x^3-27*x^2+8*x-1)/(2*x-1)^2/(x-1)^5
Generating function in latex syntax:
\frac{2 x^{8}-4 x^{7}-9 x^{6}+29 x^{5}-48 x^{4}+48 x^{3}-27 x^{2}+8 x -1}{\left(2 x -1\right)^{2} \left(x -1\right)^{5}}
Generating function in sympy syntax:
(2*x**8 - 4*x**7 - 9*x**6 + 29*x**5 - 48*x**4 + 48*x**3 - 27*x**2 + 8*x - 1)/((x - 1)**5*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
-(2*x-1)^2*(x-1)^5*F(x)+2*x^8-4*x^7-9*x^6+29*x^5-48*x^4+48*x^3-27*x^2+8*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right)^{2} \left(x -1\right)^{5} F \! \left(x \right)+2 x^{8}-4 x^{7}-9 x^{6}+29 x^{5}-48 x^{4}+48 x^{3}-27 x^{2}+8 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,-1+1/4*2^n*n-1/12*n^2+4/3*n-1/3*n^3+1/12*n^4)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ -1+\frac{2^{n} n}{4}-\frac{n^{2}}{12}+\frac{4 n}{3}-\frac{n^{3}}{3}+\frac{n^{4}}{12} & \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) = 136
a(7) = 314
a(8) = 687
a(n+2) = -4*a(n)+4*a(n+1)+1/12*(-1+n)*(n^3-11*n^2+12*n+48), 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) = 136
a \! \left(7\right) = 314
a \! \left(8\right) = 687
a \! \left(n +2\right) = -4 a \! \left(n \right)+4 a \! \left(n +1\right)+\frac{\left(-1+n \right) \left(n^{3}-11 n^{2}+12 n +48\right)}{12}, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18175/
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[19,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[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[14,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[13,x]
F[19,x] = F[20,x]+F[41,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[5,x]
F[23,x] = F[14,x]+F[24,x]
F[24,x] = F[25,x]+F[26,x]+F[28,x]
F[25,x] = 0
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[24,x]+F[6,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = F[30,x]+F[35,x]
F[30,x] = F[14,x]+F[31,x]
F[31,x] = F[25,x]+F[32,x]+F[34,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[10,x]+F[31,x]
F[34,x] = F[12,x]*F[30,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[37,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[14,x]+F[36,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[35,x]
F[41,x] = F[25,x]+F[42,x]+F[73,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[44,x]+F[51,x]
F[44,x] = F[45,x]+F[6,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[48,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[52,x]+F[63,x]
F[52,x] = F[25,x]+F[53,x]+F[55,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[52,x]+F[6,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[30,x]+F[57,x]
F[57,x] = F[58,x]+F[61,x]
F[58,x] = F[25,x]+F[37,x]+F[59,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[14,x]+F[58,x]
F[61,x] = F[62,x]
F[62,x] = F[12,x]*F[57,x]
F[63,x] = 2*F[25,x]+F[64,x]+F[66,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[45,x]+F[63,x]
F[66,x] = F[12,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[31,x]+F[69,x]
F[69,x] = 2*F[25,x]+F[70,x]+F[72,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[49,x]+F[69,x]
F[72,x] = F[12,x]*F[68,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[75,x]+F[86,x]
F[75,x] = F[20,x]+F[76,x]
F[76,x] = F[25,x]+F[77,x]+F[85,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[79,x]+F[81,x]
F[79,x] = F[10,x]+F[80,x]
F[80,x] = F[46,x]
F[81,x] = F[31,x]+F[82,x]
F[82,x] = 2*F[25,x]+F[66,x]+F[83,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[80,x]+F[82,x]
F[85,x] = F[12,x]*F[75,x]
F[86,x] = F[112,x]+F[87,x]
F[87,x] = F[25,x]+F[37,x]+F[88,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[90,x]+F[97,x]
F[90,x] = F[14,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[12,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[12,x]*F[94,x]
F[97,x] = F[58,x]+F[98,x]
F[98,x] = 2*F[25,x]+F[101,x]+F[99,x]
F[99,x] = F[100,x]*F[12,x]
F[100,x] = F[91,x]+F[98,x]
F[101,x] = F[102,x]*F[12,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]+F[108,x]
F[104,x] = F[105,x]+F[107,x]+F[25,x]
F[105,x] = F[106,x]*F[12,x]
F[106,x] = F[104,x]+F[12,x]
F[107,x] = F[12,x]*F[14,x]
F[108,x] = 2*F[25,x]+F[109,x]+F[111,x]
F[109,x] = F[110,x]*F[12,x]
F[110,x] = F[108,x]+F[95,x]
F[111,x] = F[103,x]*F[12,x]
F[112,x] = F[113,x]
F[113,x] = F[12,x]*F[86,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_{19}\! \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_{17}\! \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_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{5}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{24}\! \left(x \right)+F_{6}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{35}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)+F_{32}\! \left(x \right)+F_{34}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{10}\! \left(x \right)+F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{41}\! \left(x \right) = F_{25}\! \left(x \right)+F_{42}\! \left(x \right)+F_{73}\! \left(x \right)
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_{51}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{6}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \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_{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_{52}\! \left(x \right)+F_{63}\! \left(x \right)
F_{52}\! \left(x \right) = F_{25}\! \left(x \right)+F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{52}\! \left(x \right)+F_{6}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{30}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = F_{25}\! \left(x \right)+F_{37}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{14}\! \left(x \right)+F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{63}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{64}\! \left(x \right)+F_{66}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{45}\! \left(x \right)+F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{31}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{49}\! \left(x \right)+F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{86}\! \left(x \right)
F_{75}\! \left(x \right) = F_{20}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{25}\! \left(x \right)+F_{77}\! \left(x \right)+F_{85}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{81}\! \left(x \right)
F_{79}\! \left(x \right) = F_{10}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{46}\! \left(x \right)
F_{81}\! \left(x \right) = F_{31}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{66}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{80}\! \left(x \right)+F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{86}\! \left(x \right) = F_{112}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{25}\! \left(x \right)+F_{37}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{97}\! \left(x \right)
F_{90}\! \left(x \right) = F_{14}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{97}\! \left(x \right) = F_{58}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{101}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{12}\! \left(x \right)
F_{100}\! \left(x \right) = F_{91}\! \left(x \right)+F_{98}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{108}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{107}\! \left(x \right)+F_{25}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{12}\! \left(x \right)
F_{106}\! \left(x \right) = F_{104}\! \left(x \right)+F_{12}\! \left(x \right)
F_{107}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{108}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{109}\! \left(x \right)+F_{111}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{12}\! \left(x \right)
F_{110}\! \left(x \right) = F_{108}\! \left(x \right)+F_{95}\! \left(x \right)
F_{111}\! \left(x \right) = F_{103}\! \left(x \right) F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{12}\! \left(x \right) F_{86}\! \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_19(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_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_14(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_13(x))
Eq(F_19(x), F_20(x) + F_41(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_5(x))
Eq(F_23(x), F_14(x) + F_24(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_28(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_24(x) + F_6(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_35(x))
Eq(F_30(x), F_14(x) + F_31(x))
Eq(F_31(x), F_25(x) + F_32(x) + F_34(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_10(x) + F_31(x))
Eq(F_34(x), F_12(x)*F_30(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_14(x) + F_36(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_35(x))
Eq(F_41(x), F_25(x) + F_42(x) + F_73(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_51(x))
Eq(F_44(x), F_45(x) + F_6(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_48(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_52(x) + F_63(x))
Eq(F_52(x), F_25(x) + F_53(x) + F_55(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_52(x) + F_6(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_30(x) + F_57(x))
Eq(F_57(x), F_58(x) + F_61(x))
Eq(F_58(x), F_25(x) + F_37(x) + F_59(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_14(x) + F_58(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_12(x)*F_57(x))
Eq(F_63(x), 2*F_25(x) + F_64(x) + F_66(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_45(x) + F_63(x))
Eq(F_66(x), F_12(x)*F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_31(x) + F_69(x))
Eq(F_69(x), 2*F_25(x) + F_70(x) + F_72(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_49(x) + F_69(x))
Eq(F_72(x), F_12(x)*F_68(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_86(x))
Eq(F_75(x), F_20(x) + F_76(x))
Eq(F_76(x), F_25(x) + F_77(x) + F_85(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_81(x))
Eq(F_79(x), F_10(x) + F_80(x))
Eq(F_80(x), F_46(x))
Eq(F_81(x), F_31(x) + F_82(x))
Eq(F_82(x), 2*F_25(x) + F_66(x) + F_83(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_80(x) + F_82(x))
Eq(F_85(x), F_12(x)*F_75(x))
Eq(F_86(x), F_112(x) + F_87(x))
Eq(F_87(x), F_25(x) + F_37(x) + F_88(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_97(x))
Eq(F_90(x), F_14(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_12(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_12(x)*F_94(x))
Eq(F_97(x), F_58(x) + F_98(x))
Eq(F_98(x), F_101(x) + 2*F_25(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_12(x))
Eq(F_100(x), F_91(x) + F_98(x))
Eq(F_101(x), F_102(x)*F_12(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x) + F_108(x))
Eq(F_104(x), F_105(x) + F_107(x) + F_25(x))
Eq(F_105(x), F_106(x)*F_12(x))
Eq(F_106(x), F_104(x) + F_12(x))
Eq(F_107(x), F_12(x)*F_14(x))
Eq(F_108(x), F_109(x) + F_111(x) + 2*F_25(x))
Eq(F_109(x), F_110(x)*F_12(x))
Eq(F_110(x), F_108(x) + F_95(x))
Eq(F_111(x), F_103(x)*F_12(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_12(x)*F_86(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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 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": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 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], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "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]]}], "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": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 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], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "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], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 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], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "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]]}], "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, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 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], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "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]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[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": [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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", 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