0123_0132_0231_0312_0321
Counting sequence:
1, 1, 2, 6, 19, 61, 197, 638, 2069, 6714, 21794, 70755, 229725, 745889, 2421850, 7863641, 25532994, 82904974, 269190547, 874055885, 2838041117, 9215060822, 29921113293, 97153242650, 315454594314, 1024274628963, 3325798821581, 10798800928441, 35063486341682, 113850424959345, 369670007675074, 1200310974960982, 3897385253713811, 12654730426478237, 41089651585069301, 133417260620190894, 433203124017016901, 1406601707949008442, 4567207056263131698, 14829628157638624739, 48151500158563341949, 156346938903248093009, 507655321722499038090, 1648346475351569974345, 5352147385326103736194, 17378313396243597872990, 56427029144612936922131, 183217412730929201108909, 594903202183211981884749, 1931638563675097639692422, 6271991018007145508262525, 20365026910168353685042842, 66124827006473993015331482, 214705964589366988474662883, 697145887818159337966368365, 2263618478561068751999196009, 7349923030485754720672432738, 23865050168880520429333356001, 77489331140049142574631379586, 251606277717448345017829194662, 816960451915827390070691051795, 2652653924414496022821111470589, 8613113188294964118699240236837, 27966602846903671846640223412446, 90806989029163070543826787111797, 294848441252688285757991835321146, 957366874935366677373638677347394, 3108550716189866742864069161921891, 10093400772589821935836505580846237, 32773066440745275899371751610047233, 106413478284377314624703793727080634, 345522393550004739663124964555966009, 1121904164484505086466773812027393474, 3642799939406874308979823066528251950, 11828097103677345765761597425032864915, 38405590046429988061395822538022206349, 124702167549492740021389351206442094205, 404905394572561117504333418229110097846, 1314719557612279135454726806444920130349, 4268867588175521712269022874056382158874, 13860925989776494866121086949841500110122, 45006143977441623192446024311314127727715, 146134031536724668477772622731578020136717, 474494219808750098100308054739846834427417, 1540673053800844102827350561621080179044498, 5002533981688444594012677102397897908794705, 16243125805445908451199590197002855304133954, 52741098190899718794749238932247969246946038, 171249270103511587860561330581620612318721171, 556042887177605534985510809511618101416063581, 1805459913457857866558935303000614802414936917, 5862291514327167710742172988514986015897024270, 19034740978066296889342763934082859366411563429, 61805415717826336048819717042324995539090608442, 200680924235061066618784174595642807512880685906, 651606867846413613690345334658346923696271342307, 2115754209539528004787841342760202768943163204541, 6869810764854219408415918880446575110051068654769, 22306135434880342627042891680330005860292635388906, 72427566794815924689506786461730781410099928220457, 235170832129651787093692501107120446998794897423618
Generating function in Maple syntax:
-(x^3+3*x^2-4*x+1)/(x^3-6*x^2+5*x-1)
Generating function in latex syntax:
-\frac{x^{3}+3 x^{2}-4 x +1}{x^{3}-6 x^{2}+5 x -1}
Generating function in sympy syntax:
(-x**3 - 3*x**2 + 4*x - 1)/(x**3 - 6*x**2 + 5*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^3-6*x^2+5*x-1)*F(x)+x^3+3*x^2-4*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{3}-6 x^{2}+5 x -1\right) F \! \left(x \right)+x^{3}+3 x^{2}-4 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/3528*((12*I*3^(1/2)-10)*(756+84*I*3^(1/2))^(2/3)-98*I*(756+84*I*3^(1/2))^(1/3)*3^(1/2)-126*(756+84*I*3^(1/2))^(1/3)+2352)*(1/504*(5*I*3^(1/2)-3)*(756+84*I*3^(1/2))^(2/3)-1/12*I*3^(1/2)*(756+84*I*3^(1/2))^(1/3)-1/12*(756+84*I*3^(1/2))^(1/3)+2)^(-n)+1/3528*((-11*I*3^(1/2)-13)*(756+84*I*3^(1/2))^(2/3)+112*I*(756+84*I*3^(1/2))^(1/3)*3^(1/2)-84*(756+84*I*3^(1/2))^(1/3)+2352)*(1/252*(-2*I*3^(1/2)-3)*(756+84*I*3^(1/2))^(2/3)+1/12*I*3^(1/2)*(756+84*I*3^(1/2))^(1/3)-1/12*(756+84*I*3^(1/2))^(1/3)+2)^(-n)-1/252*(1/6*(756+84*I*3^(1/2))^(1/3)+2+1/56*(756+84*I*3^(1/2))^(2/3)-1/504*I*3^(1/2)*(756+84*I*3^(1/2))^(2/3))^(-n)*((1/14*I*3^(1/2)-23/14)*(756+84*I*3^(1/2))^(2/3)+I*(756+84*I*3^(1/2))^(1/3)*3^(1/2)-15*(756+84*I*3^(1/2))^(1/3)-168))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(\left(12 \,\mathrm{I} \sqrt{3}-10\right) \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}-98 \,\mathrm{I} \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}} \sqrt{3}-126 \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}+2352\right) \left(\frac{\left(5 \,\mathrm{I} \sqrt{3}-3\right) \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}}{504}-\frac{\mathrm{I} \sqrt{3}\, \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}}{12}-\frac{\left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}}{12}+2\right)^{-n}}{3528}\\+\\\frac{\left(\left(-11 \,\mathrm{I} \sqrt{3}-13\right) \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}+112 \,\mathrm{I} \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}} \sqrt{3}-84 \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}+2352\right) \left(\frac{\left(-2 \,\mathrm{I} \sqrt{3}-3\right) \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}}{252}+\frac{\mathrm{I} \sqrt{3}\, \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}}{12}-\frac{\left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}}{12}+2\right)^{-n}}{3528}\\-\\\frac{\left(\frac{\left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}}{6}+2+\frac{\left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}}{56}-\frac{\mathrm{I} \sqrt{3}\, \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}}{504}\right)^{-n} \left(\left(\frac{\mathrm{I} \sqrt{3}}{14}-\frac{23}{14}\right) \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{2}{3}}+\mathrm{I} \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}} \sqrt{3}-15 \left(756+84 \,\mathrm{I} \sqrt{3}\right)^{\frac{1}{3}}-168\right)}{252} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+3) = a(n)-6*a(n+1)+5*a(n+2), n >= 4
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(n +3\right) = a \! \left(n \right)-6 a \! \left(n +1\right)+5 a \! \left(n +2\right), \quad n \geq 4
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16046/
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[4,x]
F[12,x] = F[13,x]
F[13,x] = x^2
F[14,x] = F[15,x]+F[2,x]
F[15,x] = F[16,x]+F[17,x]+F[87,x]
F[16,x] = 0
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]+F[27,x]
F[19,x] = F[20,x]+F[7,x]
F[20,x] = F[16,x]+F[21,x]+F[25,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[4,x]
F[24,x] = F[12,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[11,x]
F[27,x] = F[15,x]+F[28,x]
F[28,x] = F[16,x]+F[29,x]+F[78,x]+F[84,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[35,x]
F[31,x] = F[20,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[24,x]
F[35,x] = F[28,x]+F[36,x]
F[36,x] = F[16,x]+F[37,x]+F[41,x]+F[42,x]+F[83,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[32,x]
F[40,x] = F[36,x]
F[41,x] = 0
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[45,x]
F[45,x] = 2*F[16,x]+F[46,x]+F[58,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]+F[51,x]
F[48,x] = F[12,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[12,x]*F[4,x]
F[51,x] = F[45,x]+F[52,x]
F[52,x] = 2*F[16,x]+F[41,x]+F[53,x]+F[57,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[49,x]
F[56,x] = F[52,x]
F[57,x] = F[4,x]*F[45,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[16,x]+F[60,x]+F[82,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[65,x]
F[62,x] = F[4,x]+F[63,x]
F[63,x] = F[16,x]+F[21,x]+F[64,x]
F[64,x] = x^2
F[65,x] = F[59,x]+F[66,x]
F[66,x] = F[16,x]+F[67,x]+F[78,x]+F[81,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[71,x]
F[69,x] = F[63,x]+F[70,x]
F[70,x] = F[33,x]
F[71,x] = F[66,x]+F[72,x]
F[72,x] = F[16,x]+F[41,x]+F[42,x]+F[73,x]+F[77,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[70,x]
F[76,x] = F[72,x]
F[77,x] = 0
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[44,x]+F[80,x]
F[80,x] = F[59,x]
F[81,x] = F[4,x]*F[59,x]
F[82,x] = F[2,x]*F[4,x]
F[83,x] = 0
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]
F[86,x] = F[45,x]+F[59,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[86,x]+F[89,x]
F[89,x] = F[2,x]+F[59,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_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = x^{2}
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_{87}\! \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_{27}\! \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_{25}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)
F_{27}\! \left(x \right) = F_{15}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{16}\! \left(x \right)+F_{29}\! \left(x \right)+F_{78}\! \left(x \right)+F_{84}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{31}\! \left(x \right) = F_{20}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{24}\! \left(x \right)
F_{35}\! \left(x \right) = F_{28}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{16}\! \left(x \right)+F_{37}\! \left(x \right)+F_{41}\! \left(x \right)+F_{42}\! \left(x \right)+F_{83}\! \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_{32}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right)
F_{41}\! \left(x \right) = 0
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_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{46}\! \left(x \right)+F_{58}\! \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_{51}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \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_{4}\! \left(x \right)
F_{51}\! \left(x \right) = F_{45}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{41}\! \left(x \right)+F_{53}\! \left(x \right)+F_{57}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{49}\! \left(x \right)
F_{56}\! \left(x \right) = F_{52}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{16}\! \left(x \right)+F_{60}\! \left(x \right)+F_{82}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{16}\! \left(x \right)+F_{21}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = x^{2}
F_{65}\! \left(x \right) = F_{59}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{16}\! \left(x \right)+F_{67}\! \left(x \right)+F_{78}\! \left(x \right)+F_{81}\! \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_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{63}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{33}\! \left(x \right)
F_{71}\! \left(x \right) = F_{66}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{16}\! \left(x \right)+F_{41}\! \left(x \right)+F_{42}\! \left(x \right)+F_{73}\! \left(x \right)+F_{77}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{70}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = 0
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{44}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{59}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{82}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{83}\! \left(x \right) = 0
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{45}\! \left(x \right)+F_{59}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{2}\! \left(x \right)+F_{59}\! \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_4(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), x**2)
Eq(F_14(x), F_15(x) + F_2(x))
Eq(F_15(x), F_16(x) + F_17(x) + F_87(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x) + F_27(x))
Eq(F_19(x), F_20(x) + F_7(x))
Eq(F_20(x), F_16(x) + F_21(x) + F_25(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_4(x))
Eq(F_24(x), F_12(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_11(x))
Eq(F_27(x), F_15(x) + F_28(x))
Eq(F_28(x), F_16(x) + F_29(x) + F_78(x) + F_84(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_35(x))
Eq(F_31(x), F_20(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_24(x))
Eq(F_35(x), F_28(x) + F_36(x))
Eq(F_36(x), F_16(x) + F_37(x) + F_41(x) + F_42(x) + F_83(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_32(x))
Eq(F_40(x), F_36(x))
Eq(F_41(x), 0)
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), 2*F_16(x) + F_46(x) + F_58(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_51(x))
Eq(F_48(x), F_12(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_12(x)*F_4(x))
Eq(F_51(x), F_45(x) + F_52(x))
Eq(F_52(x), 2*F_16(x) + F_41(x) + F_53(x) + F_57(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_49(x))
Eq(F_56(x), F_52(x))
Eq(F_57(x), F_4(x)*F_45(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_16(x) + F_60(x) + F_82(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_65(x))
Eq(F_62(x), F_4(x) + F_63(x))
Eq(F_63(x), F_16(x) + F_21(x) + F_64(x))
Eq(F_64(x), x**2)
Eq(F_65(x), F_59(x) + F_66(x))
Eq(F_66(x), F_16(x) + F_67(x) + F_78(x) + F_81(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_71(x))
Eq(F_69(x), F_63(x) + F_70(x))
Eq(F_70(x), F_33(x))
Eq(F_71(x), F_66(x) + F_72(x))
Eq(F_72(x), F_16(x) + F_41(x) + F_42(x) + F_73(x) + F_77(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_70(x))
Eq(F_76(x), F_72(x))
Eq(F_77(x), 0)
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_44(x) + F_80(x))
Eq(F_80(x), F_59(x))
Eq(F_81(x), F_4(x)*F_59(x))
Eq(F_82(x), F_2(x)*F_4(x))
Eq(F_83(x), 0)
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_45(x) + F_59(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_86(x) + F_89(x))
Eq(F_89(x), F_2(x) + F_59(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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 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, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "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, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"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, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"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, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [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], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [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], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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