0123_0132_0213_1302_2130
Counting sequence:
1, 1, 2, 6, 19, 54, 143, 364, 908, 2238, 5476, 13337, 32386, 78489, 189977, 459433, 1110443, 2682906, 6480439, 15650552, 37792492, 91253250, 220327652, 531954925, 1284312530, 3100701381, 7485911713, 18072842621, 43632111187, 105337897038, 254309251535, 613958578420, 1482229932956, 3578424147222, 8639087454868, 20856613987313, 50352339587314, 121561332250113, 293475067333529, 708511569251329, 1710498371416331, 4129508579998290, 9969515964907351, 24068541211221728, 58106599522253980, 140281742092041594, 338670086677552244, 817621920254673061, 1973913934965640418, 4765449802772222925, 11504813560875097345, 27775076957473697717, 67054967529138783955, 161885012102018836902, 390824991872760320207, 943534996073390911036, 2277894984384977438444, 5499324965434632517806, 13276544916210964500100, 32052414799404570273929, 77381374517524835829922, 186815163838506981471657, 451011702201096269093081, 1088838568251309729515545, 2628688838720883408301739, 6346216245720854436154314, 15321121330207537850823223, 36988458906208653598048904, 89298039142742514077382028, 215584537191884074243522098, 520467113526818724085596356, 1256518764246019976426594077, 3033504642019665192471833906, 7323528048286655330915190549, 17680560738595087339380193057, 42684649525480246464298483373, 103049859789561108207678044563, 248784369104611407273978363966, 600618597998798395089659448719, 1450021565102231614181645729092, 3500661728203299512515324050812, 8451345021508891945003015442310, 20403351771221182597374449690932, 49258048563951417640395731191265, 118919448899124277573662823196050, 287096946362200392983862105073041, 693113341623525743433024671954393, 1673323629609252979937689815083761, 4039760600842033483287820306836107, 9752844831293322826580524799572098, 23545450263428683796495480281510615, 56843745358150697959685290108939760, 137232940979730091916026475621266876, 331309627317610901532012461219696682, 799852195614951926920486033050760148, 1931014018547514807053693382179540053, 4661880232709981624649016287258263234, 11254774483967478191653578301402812573, 27171429200644938226879168724619057409, 65597632885257354999636763929902842469, 158366694971159648799300540598241826451
Generating function in Maple syntax:
(x^8+3*x^7+3*x^6+x^5-2*x^4-4*x^3-x^2+3*x-1)/(-1+x)/(x^2+x-1)/(x^2+2*x-1)
Generating function in latex syntax:
\frac{x^{8}+3 x^{7}+3 x^{6}+x^{5}-2 x^{4}-4 x^{3}-x^{2}+3 x -1}{\left(-1+x \right) \left(x^{2}+x -1\right) \left(x^{2}+2 x -1\right)}
Generating function in sympy syntax:
(x**8 + 3*x**7 + 3*x**6 + x**5 - 2*x**4 - 4*x**3 - x**2 + 3*x - 1)/((x - 1)*(x**2 + x - 1)*(x**2 + 2*x - 1))
Implicit equation for the generating function in Maple syntax:
-(-1+x)*(x^2+x-1)*(x^2+2*x-1)*F(x)+x^8+3*x^7+3*x^6+x^5-2*x^4-4*x^3-x^2+3*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(-1+x \right) \left(x^{2}+x -1\right) \left(x^{2}+2 x -1\right) F \! \left(x \right)+x^{8}+3 x^{7}+3 x^{6}+x^{5}-2 x^{4}-4 x^{3}-x^{2}+3 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,-1,n = 1,4,Or(n = 2,n = 3),1,0)-3/2-3/10*(1/2*5^(1/2)-1/2)^(-n)*5^(1/2)-(2^(1/2)-1)^(-n)*2^(1/2)+(-1-2^(1/2))^(-n)*2^(1/2)+3/10*(-1/2*5^(1/2)-1/2)^(-n)*5^(1/2)-1/2*(1/2*5^(1/2)-1/2)^(-n)+9/4*(2^(1/2)-1)^(-n)+9/4*(-1-2^(1/2))^(-n)-1/2*(-1/2*5^(1/2)-1/2)^(-n)
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}-1 & n =0 \\ 4 & n =1 \\ 1 & n =2\text{ or } n =3 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)-\frac{3}{2}-\frac{3 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n} \sqrt{5}}{10}-\left(\sqrt{2}-1\right)^{-n} \sqrt{2}+\left(-1-\sqrt{2}\right)^{-n} \sqrt{2}+\frac{3 \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n} \sqrt{5}}{10}-\frac{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{2}+\frac{9 \left(\sqrt{2}-1\right)^{-n}}{4}+\frac{9 \left(-1-\sqrt{2}\right)^{-n}}{4}-\frac{\left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{2}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 54
a(6) = 143
a(7) = 364
a(8) = 908
a(n+1) = -1/3*a(n)+a(n+3)-1/3*a(n+4)-1, 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) = 143
a \! \left(7\right) = 364
a \! \left(8\right) = 908
a \! \left(n +1\right) = -\frac{a \! \left(n \right)}{3}+a \! \left(n +3\right)-\frac{a \! \left(n +4\right)}{3}-1, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16011/
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[14,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[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[7,x]
F[12,x] = F[13,x]
F[13,x] = F[4,x]*F[7,x]
F[14,x] = F[15,x]+F[2,x]
F[15,x] = F[16,x]+F[17,x]+F[71,x]
F[16,x] = 0
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]+F[29,x]
F[19,x] = F[20,x]+F[7,x]
F[20,x] = F[16,x]+F[21,x]+F[23,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[4,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[11,x]+F[25,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[23,x]
F[27,x] = F[28,x]
F[28,x] = F[26,x]*F[4,x]
F[29,x] = F[30,x]+F[62,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[35,x]
F[33,x] = F[34,x]+F[7,x]
F[34,x] = F[21,x]
F[35,x] = F[30,x]+F[36,x]
F[36,x] = 2*F[16,x]+F[37,x]+F[45,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[34,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[34,x]
F[44,x] = F[41,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[52,x]
F[50,x] = F[4,x]+F[51,x]
F[51,x] = F[21,x]
F[52,x] = F[47,x]+F[53,x]
F[53,x] = 2*F[16,x]+F[45,x]+F[54,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[51,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[61,x]
F[60,x] = F[51,x]
F[61,x] = F[58,x]
F[62,x] = 2*F[16,x]+F[45,x]+F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[20,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[20,x]
F[70,x] = F[67,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]+F[90,x]
F[73,x] = F[2,x]+F[74,x]
F[74,x] = F[16,x]+F[75,x]+F[89,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]+F[79,x]
F[77,x] = F[4,x]+F[78,x]
F[78,x] = F[13,x]+F[16,x]+F[21,x]
F[79,x] = F[47,x]+F[80,x]
F[80,x] = 2*F[16,x]+F[45,x]+F[81,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[78,x]
F[84,x] = F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[87,x]+F[88,x]
F[87,x] = F[78,x]
F[88,x] = F[85,x]
F[89,x] = F[2,x]*F[4,x]
F[90,x] = F[91,x]+F[99,x]
F[91,x] = F[92,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[94,x]+F[96,x]
F[94,x] = F[2,x]+F[95,x]
F[95,x] = F[89,x]
F[96,x] = F[91,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[4,x]*F[91,x]
F[99,x] = F[98,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_{14}\! \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_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{71}\! \left(x \right)
F_{16}\! \left(x \right) = 0
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{29}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{7}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{62}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{35}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{7}\! \left(x \right)
F_{34}\! \left(x \right) = F_{21}\! \left(x \right)
F_{35}\! \left(x \right) = F_{30}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{37}\! \left(x \right)+F_{45}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{34}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{34}\! \left(x \right)
F_{44}\! \left(x \right) = F_{41}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{52}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{21}\! \left(x \right)
F_{52}\! \left(x \right) = F_{47}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{45}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{51}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{61}\! \left(x \right)
F_{60}\! \left(x \right) = F_{51}\! \left(x \right)
F_{61}\! \left(x \right) = F_{58}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{45}\! \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_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{20}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right)
F_{70}\! \left(x \right) = F_{67}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{90}\! \left(x \right)
F_{73}\! \left(x \right) = F_{2}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{16}\! \left(x \right)+F_{75}\! \left(x \right)+F_{89}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{79}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{13}\! \left(x \right)+F_{16}\! \left(x \right)+F_{21}\! \left(x \right)
F_{79}\! \left(x \right) = F_{47}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{45}\! \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_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{78}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{88}\! \left(x \right)
F_{87}\! \left(x \right) = F_{78}\! \left(x \right)
F_{88}\! \left(x \right) = F_{85}\! \left(x \right)
F_{89}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{99}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{96}\! \left(x \right)
F_{94}\! \left(x \right) = F_{2}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{89}\! \left(x \right)
F_{96}\! \left(x \right) = F_{91}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{99}\! \left(x \right) = F_{98}\! \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_14(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_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_7(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_4(x)*F_7(x))
Eq(F_14(x), F_15(x) + F_2(x))
Eq(F_15(x), F_16(x) + F_17(x) + F_71(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x) + F_29(x))
Eq(F_19(x), F_20(x) + F_7(x))
Eq(F_20(x), F_16(x) + F_21(x) + F_23(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_4(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_11(x) + F_25(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_23(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_26(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_62(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_35(x))
Eq(F_33(x), F_34(x) + F_7(x))
Eq(F_34(x), F_21(x))
Eq(F_35(x), F_30(x) + F_36(x))
Eq(F_36(x), 2*F_16(x) + F_37(x) + F_45(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_34(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_34(x))
Eq(F_44(x), F_41(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_52(x))
Eq(F_50(x), F_4(x) + F_51(x))
Eq(F_51(x), F_21(x))
Eq(F_52(x), F_47(x) + F_53(x))
Eq(F_53(x), 2*F_16(x) + F_45(x) + F_54(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_51(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_61(x))
Eq(F_60(x), F_51(x))
Eq(F_61(x), F_58(x))
Eq(F_62(x), 2*F_16(x) + F_45(x) + F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_20(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_20(x))
Eq(F_70(x), F_67(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_90(x))
Eq(F_73(x), F_2(x) + F_74(x))
Eq(F_74(x), F_16(x) + F_75(x) + F_89(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_79(x))
Eq(F_77(x), F_4(x) + F_78(x))
Eq(F_78(x), F_13(x) + F_16(x) + F_21(x))
Eq(F_79(x), F_47(x) + F_80(x))
Eq(F_80(x), 2*F_16(x) + F_45(x) + F_81(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_78(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_88(x))
Eq(F_87(x), F_78(x))
Eq(F_88(x), F_85(x))
Eq(F_89(x), F_2(x)*F_4(x))
Eq(F_90(x), F_91(x) + F_99(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_96(x))
Eq(F_94(x), F_2(x) + F_95(x))
Eq(F_95(x), F_89(x))
Eq(F_96(x), F_91(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_4(x)*F_91(x))
Eq(F_99(x), F_98(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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