0231_0321_2103_3021
Counting sequence:
1, 1, 2, 6, 20, 64, 189, 524, 1396, 3633, 9323, 23707, 59889, 150536, 376903, 940755, 2342414, 5821180, 14444082, 35795990, 88623715, 219240390, 542017406, 1339311703, 3308026701, 8167891985, 20161952479, 49757595942, 122774629001, 302897057053, 747189197652, 1842998045558, 4545542671528, 11210358664044, 27645936660713, 68175023788192, 168114372743256, 414545951818013, 1022188554527935, 2520470656466583, 6214783867110941, 15323760166555108, 37783357933786347, 93160631771144375, 229700316450194458, 566354777816181696, 1396412618466720974, 3443003922415625458, 8489069707335575343, 20930602625780603546, 51606284839923946882, 127239757565264561859, 313720258363710455681, 773502788998151118061, 1907132514569566407339, 4702183643778082461890, 11593593880057833276589, 28584881866647384241953, 70478163040830146416544, 173769132556648221178138, 428440576795166419139556, 1056351565865479237484840, 2604511641847157972911285, 6421612197828991871910132, 15832948738441129156079612, 39037275807690058824583561, 96249209967099620415830355, 237309334715387685572969939, 585103171789355037815133577, 1442613754162245026900485440, 3556867383209296859759803151, 8769710720115885187011424987, 21622348112347507068006618150, 53311442769325923992365712324, 131443166217688678342697943850, 324082502444717338917450888846, 799048521165503184542346614267, 1970111099425690975828097126638, 4857449355877797791788750666182, 11976387603216041430513042003119, 29528637158425840868335676318965, 72804959138603732051629687773705, 179505814478628212867351376539063, 442584375510160443238207858303966, 1091223310690089363614851137960273, 2690488815898994794558194438175589, 6633591851183123525248695734287084, 16355593286322007889799464353099518, 40325880395097837658131162441385952, 99426330818387560442277815974700452, 245142701389140834513862646294756481, 604416793114146563550472595716853192, 1490232658894499792423445805492074976, 3674274776031598914411078594616989813, 9059186192710156504034643962855516711, 22336068874793771057065801944208088143, 55071168878574378922747787045195229237, 135781889748169690860615196945886007836, 334779921283609303885617511585350112435, 825423743148154141779033929137872023871, 2035141035656763607812686762243027407922
Generating function in Maple syntax:
(2*x^7-2*x^6-10*x^5+24*x^4-29*x^3+20*x^2-7*x+1)/(2*x-1)/(3*x^3-5*x^2+4*x-1)/(x-1)^2
Generating function in latex syntax:
\frac{2 x^{7}-2 x^{6}-10 x^{5}+24 x^{4}-29 x^{3}+20 x^{2}-7 x +1}{\left(2 x -1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(2*x**7 - 2*x**6 - 10*x**5 + 24*x**4 - 29*x**3 + 20*x**2 - 7*x + 1)/((x - 1)**2*(2*x - 1)*(3*x**3 - 5*x**2 + 4*x - 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(3*x^3-5*x^2+4*x-1)*(x-1)^2*F(x)+2*x^7-2*x^6-10*x^5+24*x^4-29*x^3+20*x^2-7*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+2 x^{7}-2 x^{6}-10 x^{5}+24 x^{4}-29 x^{3}+20 x^{2}-7 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/405108*(-2263*2^(1/3)*((I+339/2263*31^(1/2))*3^(1/2)+1017/2263*I*31^(1/2)+1)*(47+9*31^(1/2)*3^(1/2))^(2/3)+195052-17732*((I+75/806*31^(1/2))*3^(1/2)-225/806*I*31^(1/2)-1)*2^(2/3)*(47+9*31^(1/2)*3^(1/2))^(1/3))*(47/8712*2^(1/3)*((I-9/47*31^(1/2))*3^(1/2)-27/47*I*31^(1/2)+1)*(47+9*31^(1/2)*3^(1/2))^(2/3)-1/36*I*3^(1/2)*(188+36*31^(1/2)*3^(1/2))^(1/3)+1/36*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/405108*(17732*2^(2/3)*((I-75/806*31^(1/2))*3^(1/2)-225/806*I*31^(1/2)+1)*(47+9*31^(1/2)*3^(1/2))^(1/3)+195052+2263*2^(1/3)*((I-339/2263*31^(1/2))*3^(1/2)+1017/2263*I*31^(1/2)-1)*(47+9*31^(1/2)*3^(1/2))^(2/3))*(-47/8712*((I+9/47*31^(1/2))*3^(1/2)-27/47*I*31^(1/2)-1)*2^(1/3)*(47+9*31^(1/2)*3^(1/2))^(2/3)+1/36*I*3^(1/2)*(188+36*31^(1/2)*3^(1/2))^(1/3)+1/36*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/405108*((3300*2^(2/3)*31^(1/2)*3^(1/2)-35464*2^(2/3))*(47+9*31^(1/2)*3^(1/2))^(1/3)+195052+(678*31^(1/2)*3^(1/2)*2^(1/3)+4526*2^(1/3))*(47+9*31^(1/2)*3^(1/2))^(2/3))*(1/4356*2^(1/3)*(9*31^(1/2)*3^(1/2)-47)*(47+9*31^(1/2)*3^(1/2))^(2/3)-1/18*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)-n-3*2^(-1+n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(-2263 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{339 \sqrt{31}}{2263}\right) \sqrt{3}+\frac{1017 \,\mathrm{I} \sqrt{31}}{2263}+1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}+195052-17732 \left(\left(\mathrm{I}+\frac{75 \sqrt{31}}{806}\right) \sqrt{3}-\frac{225 \,\mathrm{I} \sqrt{31}}{806}-1\right) 2^{\frac{2}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{47 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{9 \sqrt{31}}{47}\right) \sqrt{3}-\frac{27 \,\mathrm{I} \sqrt{31}}{47}+1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{8712}-\frac{\mathrm{I} \sqrt{3}\, \left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{5}{9}\right)^{-n}}{405108}\\+\\\frac{\left(17732 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}-\frac{75 \sqrt{31}}{806}\right) \sqrt{3}-\frac{225 \,\mathrm{I} \sqrt{31}}{806}+1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+195052+2263 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{339 \sqrt{31}}{2263}\right) \sqrt{3}+\frac{1017 \,\mathrm{I} \sqrt{31}}{2263}-1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{47 \left(\left(\mathrm{I}+\frac{9 \sqrt{31}}{47}\right) \sqrt{3}-\frac{27 \,\mathrm{I} \sqrt{31}}{47}-1\right) 2^{\frac{1}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{8712}+\frac{\mathrm{I} \sqrt{3}\, \left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{5}{9}\right)^{-n}}{405108}\\+\\\frac{\left(\left(3300 \,2^{\frac{2}{3}} \sqrt{31}\, \sqrt{3}-35464 \,2^{\frac{2}{3}}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+195052+\left(678 \sqrt{31}\, \sqrt{3}\, 2^{\frac{1}{3}}+4526 \,2^{\frac{1}{3}}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{2^{\frac{1}{3}} \left(9 \sqrt{31}\, \sqrt{3}-47\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{4356}-\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{18}+\frac{5}{9}\right)^{-n}}{405108}\\-n -3 \,2^{-1+n} & \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) = 64
a(6) = 189
a(7) = 524
a(n+4) = -6*a(n)+13*a(n+1)-13*a(n+2)+6*a(n+3)+1-n, 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) = 64
a \! \left(6\right) = 189
a \! \left(7\right) = 524
a \! \left(n +4\right) = -6 a \! \left(n \right)+13 a \! \left(n +1\right)-13 a \! \left(n +2\right)+6 a \! \left(n +3\right)+1-n, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15849/
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[17,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[6,x]
F[10,x] = F[11,x]+F[14,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[11,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[14,x]+F[7,x]
F[17,x] = F[18,x]+F[36,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[13,x]+F[21,x]
F[21,x] = F[18,x]+F[22,x]
F[22,x] = F[23,x]+F[24,x]+F[35,x]
F[23,x] = 0
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[11,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[26,x]*F[4,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[18,x]+F[30,x]
F[33,x] = F[34,x]
F[34,x] = F[29,x]*F[4,x]
F[35,x] = F[21,x]*F[4,x]
F[36,x] = F[23,x]+F[37,x]+F[69,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[48,x]
F[39,x] = F[40,x]+F[7,x]
F[40,x] = F[23,x]+F[41,x]+F[42,x]
F[41,x] = F[39,x]*F[4,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[10,x]+F[44,x]
F[44,x] = F[27,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[14,x]+F[45,x]
F[48,x] = F[49,x]+F[57,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[18,x]+F[49,x]
F[53,x] = F[30,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[49,x]+F[54,x]
F[57,x] = 2*F[23,x]+F[58,x]+F[59,x]
F[58,x] = F[4,x]*F[48,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[65,x]
F[61,x] = F[22,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[49,x]+F[62,x]
F[65,x] = F[33,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[54,x]+F[66,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[17,x]+F[71,x]
F[71,x] = F[22,x]+F[72,x]
F[72,x] = 2*F[23,x]+F[63,x]+F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[75,x]+F[78,x]
F[75,x] = F[14,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[4,x]*F[75,x]
F[78,x] = F[54,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[4,x]*F[78,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_{17}\! \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_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{36}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{35}\! \left(x \right)
F_{23}\! \left(x \right) = 0
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \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_{33}\! \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_{18}\! \left(x \right)+F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{23}\! \left(x \right)+F_{37}\! \left(x \right)+F_{69}\! \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_{48}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{7}\! \left(x \right)
F_{40}\! \left(x \right) = F_{23}\! \left(x \right)+F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{10}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{27}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{14}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{57}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{18}\! \left(x \right)+F_{49}\! \left(x \right)
F_{53}\! \left(x \right) = F_{30}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{49}\! \left(x \right)+F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{61}\! \left(x \right) = F_{22}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \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_{49}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{33}\! \left(x \right)+F_{66}\! \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_{54}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{17}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{22}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{63}\! \left(x \right)+F_{73}\! \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_{78}\! \left(x \right)
F_{75}\! \left(x \right) = F_{14}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = F_{54}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \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_17(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_6(x))
Eq(F_10(x), F_11(x) + F_14(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_11(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_14(x) + F_7(x))
Eq(F_17(x), F_18(x) + F_36(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_13(x) + F_21(x))
Eq(F_21(x), F_18(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_24(x) + F_35(x))
Eq(F_23(x), 0)
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_11(x) + F_27(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_33(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_18(x) + F_30(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_29(x)*F_4(x))
Eq(F_35(x), F_21(x)*F_4(x))
Eq(F_36(x), F_23(x) + F_37(x) + F_69(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_48(x))
Eq(F_39(x), F_40(x) + F_7(x))
Eq(F_40(x), F_23(x) + F_41(x) + F_42(x))
Eq(F_41(x), F_39(x)*F_4(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_10(x) + F_44(x))
Eq(F_44(x), F_27(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_14(x) + F_45(x))
Eq(F_48(x), F_49(x) + F_57(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_18(x) + F_49(x))
Eq(F_53(x), F_30(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_49(x) + F_54(x))
Eq(F_57(x), 2*F_23(x) + F_58(x) + F_59(x))
Eq(F_58(x), F_4(x)*F_48(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_65(x))
Eq(F_61(x), F_22(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_49(x) + F_62(x))
Eq(F_65(x), F_33(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_54(x) + F_66(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_17(x) + F_71(x))
Eq(F_71(x), F_22(x) + F_72(x))
Eq(F_72(x), 2*F_23(x) + F_63(x) + F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_78(x))
Eq(F_75(x), F_14(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_4(x)*F_75(x))
Eq(F_78(x), F_54(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_4(x)*F_78(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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"comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [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, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [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": [1, 2, 0], "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": 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1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": 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[[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "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, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "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": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 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1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "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": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, 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