0123_0132_1032_1203_3021
Counting sequence:
1, 1, 2, 6, 19, 53, 138, 347, 856, 2086, 5039, 12091, 28859, 68588, 162443, 383622, 903786, 2124991, 4987889, 11691201, 27370274, 64011223, 149574148, 349249922, 814971991, 1900708871, 4430869739, 10325037836, 24051831639, 56011786458, 130407728878, 303553435247, 706460614221, 1643890660601, 3824720107714, 8897671454371, 20697128484704, 48140090005918, 111962339208383, 260381275509347, 605513856939851, 1408050596654556, 3274123826883939, 7613021094863806, 17701340128640594, 41157049825403103, 95691385918441913, 222481189442460097, 517257428734499506, 1202580458074220111, 2795866035870521164, 6500011279546422266, 15111515543670043559, 35131656745183005263, 81674483702545746843, 189876719710522065372, 441422981570819291311, 1026210255192282657266, 2385702054542377789014, 5546189699606680012751, 12893537374514152455349, 29974259038044645805273, 69682540583058653869298, 161993938084293505155547, 376593586198193218939016, 875480611155822031186646, 2035258975448914622460239, 4731430042820375947192011, 10999294293893286474333339, 25570364781836353844058508, 59444101821239527916665403, 138191202235332489308141622, 321256431928141419479010746, 746832321300572114825130751, 1736177958611912609000945089, 4036130977825028245182449921, 9382879962876418089072321154, 21812577142240283299256470343, 50708144980091387791614141908, 117882245621266706519015652722, 274043194051051010580302837751, 637073575901097773108946735831, 1481017265243231537914160956939, 3442949198020097144562713781356, 8003889359558020263884409254919, 18606792388043286306273247336778, 43255558523366292067276209637438, 100557001914235076916491688204847, 233766724605345439047846182098781, 543441815553591467631131958368761, 1263349173449636626220796356802914, 2936930962017708431461173651148691, 6827537051048715607599464828966384, 15872099795242910782149652802919438, 36898159031014097954816820925003743, 85777820124335364691961859044197747, 199409253247681162516824062177623211, 463570300808307563258210237553713916, 1077670260619737143706634343718565139, 2505279522621960295667686410962834926, 5824068525698079819942760368478976674
Generating function in Maple syntax:
(x^7-x^6+4*x^5-3*x^4+6*x^3-9*x^2+5*x-1)/(x-1)/(2*x-1)/(x^3-2*x^2+3*x-1)
Generating function in latex syntax:
\frac{x^{7}-x^{6}+4 x^{5}-3 x^{4}+6 x^{3}-9 x^{2}+5 x -1}{\left(x -1\right) \left(2 x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right)}
Generating function in sympy syntax:
(x**7 - x**6 + 4*x**5 - 3*x**4 + 6*x**3 - 9*x**2 + 5*x - 1)/((x - 1)*(2*x - 1)*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
-(x-1)*(2*x-1)*(x^3-2*x^2+3*x-1)*F(x)+x^7-x^6+4*x^5-3*x^4+6*x^3-9*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right) \left(2 x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) F \! \left(x \right)+x^{7}-x^{6}+4 x^{5}-3 x^{4}+6 x^{3}-9 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,n = 2,2,1/13800*(-253*2^(1/3)*((31/253*23^(1/2)+I)*3^(1/2)+93/253*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(2/3)+4600-920*2^(2/3)*((11/92*23^(1/2)+I)*3^(1/2)-33/92*I*23^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(1/3))*(11/600*((I-3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)+1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)-1/12*I*3^(1/2)*(44+12*23^(1/2)*3^(1/2))^(1/3)+1/12*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/13800*(920*((-11/92*23^(1/2)+I)*3^(1/2)-33/92*I*23^(1/2)+1)*2^(2/3)*(11+3*23^(1/2)*3^(1/2))^(1/3)+4600+253*2^(1/3)*((-31/253*23^(1/2)+I)*3^(1/2)+93/253*I*23^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(2/3))*(-11/600*((I+3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)-1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+1/12*I*3^(1/2)*(44+12*23^(1/2)*3^(1/2))^(1/3)+1/12*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/13800*((220*2^(2/3)*23^(1/2)*3^(1/2)-1840*2^(2/3))*(11+3*23^(1/2)*3^(1/2))^(1/3)+4600+(62*23^(1/2)*3^(1/2)*2^(1/3)+506*2^(1/3))*(11+3*23^(1/2)*3^(1/2))^(2/3))*(1/300*2^(1/3)*(3*23^(1/2)*3^(1/2)-11)*(11+3*23^(1/2)*3^(1/2))^(2/3)-1/6*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)-9/8*2^n-2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ 2 & n =2 \\ \frac{\left(-253 \,2^{\frac{1}{3}} \left(\left(\frac{31 \sqrt{23}}{253}+\mathrm{I}\right) \sqrt{3}+\frac{93 \,\mathrm{I} \sqrt{23}}{253}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+4600-920 \,2^{\frac{2}{3}} \left(\left(\frac{11 \sqrt{23}}{92}+\mathrm{I}\right) \sqrt{3}-\frac{33 \,\mathrm{I} \sqrt{23}}{92}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{11 \left(\left(\mathrm{I}-\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}+1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{600}-\frac{\mathrm{I} \sqrt{3}\, \left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{13800}\\+\\\frac{\left(920 \left(\left(-\frac{11 \sqrt{23}}{92}+\mathrm{I}\right) \sqrt{3}-\frac{33 \,\mathrm{I} \sqrt{23}}{92}+1\right) 2^{\frac{2}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+4600+253 \,2^{\frac{1}{3}} \left(\left(-\frac{31 \sqrt{23}}{253}+\mathrm{I}\right) \sqrt{3}+\frac{93 \,\mathrm{I} \sqrt{23}}{253}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{11 \left(\left(\mathrm{I}+\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}-1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{600}+\frac{\mathrm{I} \sqrt{3}\, \left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{13800}\\+\\\frac{\left(\left(220 \,2^{\frac{2}{3}} \sqrt{23}\, \sqrt{3}-1840 \,2^{\frac{2}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+4600+\left(62 \sqrt{23}\, \sqrt{3}\, 2^{\frac{1}{3}}+506 \,2^{\frac{1}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{2^{\frac{1}{3}} \left(3 \sqrt{23}\, \sqrt{3}-11\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{300}-\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{2}{3}\right)^{-n}}{13800}\\-\frac{9 \,2^{n}}{8}-2 & \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) = 53
a(6) = 138
a(7) = 347
a(n+4) = -2*a(n)+5*a(n+1)-8*a(n+2)+5*a(n+3)-2, 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) = 19
a \! \left(5\right) = 53
a \! \left(6\right) = 138
a \! \left(7\right) = 347
a \! \left(n +4\right) = -2 a \! \left(n \right)+5 a \! \left(n +1\right)-8 a \! \left(n +2\right)+5 a \! \left(n +3\right)-2, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16343/
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[19,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[14,x]+F[18,x]
F[13,x] = 0
F[14,x] = F[15,x]*F[4,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[4,x]
F[17,x] = F[12,x]
F[18,x] = F[4,x]*F[7,x]
F[19,x] = F[20,x]+F[45,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[10,x]*F[4,x]
F[26,x] = F[20,x]+F[27,x]
F[27,x] = F[13,x]+F[28,x]+F[43,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[24,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[16,x]*F[4,x]
F[33,x] = F[27,x]+F[34,x]
F[34,x] = 2*F[13,x]+F[35,x]+F[39,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[31,x]
F[38,x] = F[34,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[20,x]*F[4,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[20,x]+F[41,x]
F[45,x] = F[13,x]+F[46,x]+F[66,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]+F[54,x]
F[48,x] = F[24,x]+F[49,x]
F[49,x] = F[13,x]+F[32,x]+F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[24,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[24,x]*F[4,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[13,x]+F[43,x]+F[46,x]
F[56,x] = F[13,x]+F[39,x]+F[57,x]+F[62,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[31,x]
F[60,x] = F[61,x]
F[61,x] = 2*F[13,x]+F[39,x]+F[57,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[27,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[27,x]*F[4,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[44,x]+F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[13,x]+F[28,x]+F[66,x]
F[70,x] = 2*F[13,x]+F[71,x]+F[74,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[40,x]+F[73,x]
F[73,x] = F[70,x]
F[74,x] = F[4,x]*F[69,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_{19}\! \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_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{13}\! \left(x \right) = 0
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right)
F_{18}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{45}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \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_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{13}\! \left(x \right)+F_{28}\! \left(x \right)+F_{43}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \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_{24}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{27}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{35}\! \left(x \right)+F_{39}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{31}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13}\! \left(x \right)+F_{46}\! \left(x \right)+F_{66}\! \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_{54}\! \left(x \right)
F_{48}\! \left(x \right) = F_{24}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{13}\! \left(x \right)+F_{32}\! \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_{24}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{13}\! \left(x \right)+F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{56}\! \left(x \right) = F_{13}\! \left(x \right)+F_{39}\! \left(x \right)+F_{57}\! \left(x \right)+F_{62}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{31}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{39}\! \left(x \right)+F_{57}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{27}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{44}\! \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_{13}\! \left(x \right)+F_{28}\! \left(x \right)+F_{66}\! \left(x \right)
F_{70}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{40}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{70}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \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_19(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) + F_14(x) + F_18(x))
Eq(F_13(x), 0)
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_4(x))
Eq(F_17(x), F_12(x))
Eq(F_18(x), F_4(x)*F_7(x))
Eq(F_19(x), F_20(x) + F_45(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_10(x)*F_4(x))
Eq(F_26(x), F_20(x) + F_27(x))
Eq(F_27(x), F_13(x) + F_28(x) + F_43(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_24(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_16(x)*F_4(x))
Eq(F_33(x), F_27(x) + F_34(x))
Eq(F_34(x), 2*F_13(x) + F_35(x) + F_39(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_31(x))
Eq(F_38(x), F_34(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_20(x)*F_4(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_20(x) + F_41(x))
Eq(F_45(x), F_13(x) + F_46(x) + F_66(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_54(x))
Eq(F_48(x), F_24(x) + F_49(x))
Eq(F_49(x), F_13(x) + F_32(x) + F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_24(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_24(x)*F_4(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_13(x) + F_43(x) + F_46(x))
Eq(F_56(x), F_13(x) + F_39(x) + F_57(x) + F_62(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_31(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), 2*F_13(x) + F_39(x) + F_57(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_27(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_27(x)*F_4(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_44(x) + F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_13(x) + F_28(x) + F_66(x))
Eq(F_70(x), 2*F_13(x) + F_71(x) + F_74(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_40(x) + F_73(x))
Eq(F_73(x), F_70(x))
Eq(F_74(x), F_4(x)*F_69(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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