0123_0132_1023_1320_2130

Counting sequence:
1, 1, 2, 6, 19, 52, 125, 276, 581, 1184, 2359, 4626, 8965, 17218, 32837, 62274, 117563, 221108, 414553, 775200, 1446373, 2693536, 5007947, 9298014, 17242397, 31941314, 59117473, 109329774, 202052779, 373192708, 688932029, 1271226828, 2344757501, 4323371456, 7969216663, 14685661434, 27056426077, 49837796338, 91784552357, 169009935258, 311168112755, 572829589460, 1054410455161, 1940677963944, 3571590632605, 6572621482096, 12094505132843, 22254274731894, 40946573885141, 75336083772290, 138602834949793, 254992125189846, 469103579054755, 862977706919572, 1587525114031901, 2920337270598852, 5372022665010389, 9881798493693536, 18177254446814935, 33436085067083106, 61503243486667669, 113129697941205730, 208090246914672293, 382757523702901170, 704033024338850123, 1294970686096849652, 2381906681059097593, 4381145729555719728, 8058403881693085621, 14822072415350243584, 27262618934622807851, 50144708262732236238, 92232009551795145389, 169643559719306145986, 312027110443079341441, 573913735593582402750, 1055602294544615473531, 1941572085249326570596, 3571134948844221382685, 6568385106762909715068, 12081214752437900891981, 22220933197751221501184, 40870854058239664842871, 75173521399422609481674, 138266149047694950805549, 254311884288632502355090, 467753754911306794846661, 860335348206466257436170, 1582406747540794296270659, 2910505170751788099614612, 5353262346726658146014809, 9846198665340070785654072, 18110005663366956767730349, 33309530556302955679599568, 61265838246427692949630667, 112685541708384585093807078, 207261181114819923136529957, 381212998915623870290306306, 701160430188524737044474049, 1289635756514656558105479078, 2372011040364189551598258355

Generating function in Maple syntax:
(x^9-x^8-6*x^7-5*x^6-x^5+3*x^4+3*x^3+2*x^2-3*x+1)/(x^2+x-1)/(x^3+x^2+x-1)/(x-1)^2

Generating function in latex syntax:
\frac{x^{9}-x^{8}-6 x^{7}-5 x^{6}-x^{5}+3 x^{4}+3 x^{3}+2 x^{2}-3 x +1}{\left(x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{2}}

Generating function in sympy syntax:
(x**9 - x**8 - 6*x**7 - 5*x**6 - x**5 + 3*x**4 + 3*x**3 + 2*x**2 - 3*x + 1)/((x - 1)**2*(x**2 + x - 1)*(x**3 + x**2 + x - 1))

Implicit equation for the generating function in Maple syntax:
-(x^2+x-1)*(x^3+x^2+x-1)*(x-1)^2*F(x)+x^9-x^8-6*x^7-5*x^6-x^5+3*x^4+3*x^3+2*x^2-3*x+1 = 0

Implicit equation for the generating function in latex syntax:
-\left(x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+x^{9}-x^{8}-6 x^{7}-5 x^{6}-x^{5}+3 x^{4}+3 x^{3}+2 x^{2}-3 x +1 = 0

Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,n = 2,2,1/440*(((-90*11^(1/2)+330*I)*3^(1/2)-270*I*11^(1/2)+330)*(17+3*11^(1/2)*3^(1/2))^(1/3)+1320+((135*11^(1/2)+825*I)*3^(1/2)-405*I*11^(1/2)-825)*(17+3*11^(1/2)*3^(1/2))^(2/3))*(1/24*((17*I+3*11^(1/2))*3^(1/2)-9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/440*(((135*11^(1/2)-825*I)*3^(1/2)+405*I*11^(1/2)-825)*(17+3*11^(1/2)*3^(1/2))^(2/3)+1320+((-90*11^(1/2)-330*I)*3^(1/2)+270*I*11^(1/2)+330)*(17+3*11^(1/2)*3^(1/2))^(1/3))*(1/24*((-17*I+3*11^(1/2))*3^(1/2)+9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)+1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/440*((-270*11^(1/2)*3^(1/2)+1650)*(17+3*11^(1/2)*3^(1/2))^(2/3)+180*(17+3*11^(1/2)*3^(1/2))^(1/3)*11^(1/2)*3^(1/2)-660*(17+3*11^(1/2)*3^(1/2))^(1/3)+1320)*(1/3*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3+17/12*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/4*(17+3*11^(1/2)*3^(1/2))^(2/3)*11^(1/2)*3^(1/2))^(-n)+1/440*(968*5^(1/2)-2200)*(-1/2*5^(1/2)-1/2)^(-n)+1/440*(-968*5^(1/2)-2200)*(1/2*5^(1/2)-1/2)^(-n)-3*n+6)

Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ 2 & n =2 \\ \frac{\left(\left(\left(-90 \sqrt{11}+330 \,\mathrm{I}\right) \sqrt{3}-270 \,\mathrm{I} \sqrt{11}+330\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+1320+\left(\left(135 \sqrt{11}+825 \,\mathrm{I}\right) \sqrt{3}-405 \,\mathrm{I} \sqrt{11}-825\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}-9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}-\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{440}\\+\\\frac{\left(\left(\left(135 \sqrt{11}-825 \,\mathrm{I}\right) \sqrt{3}+405 \,\mathrm{I} \sqrt{11}-825\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+1320+\left(\left(-90 \sqrt{11}-330 \,\mathrm{I}\right) \sqrt{3}+270 \,\mathrm{I} \sqrt{11}+330\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{\left(\left(-17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}+9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}+\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{440}\\+\\\frac{\left(\left(-270 \sqrt{11}\, \sqrt{3}+1650\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+180 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{11}\, \sqrt{3}-660 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+1320\right) \left(\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{3}-\frac{1}{3}+\frac{17 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{12}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{11}\, \sqrt{3}}{4}\right)^{-n}}{440}\\+\frac{\left(968 \sqrt{5}-2200\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{440}+\frac{\left(-968 \sqrt{5}-2200\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{440}-\\3 n +6 & \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) = 52
a(6) = 125
a(7) = 276
a(8) = 581
a(9) = 1184
a(n+5) = -a(n)-2*a(n+1)-a(n+2)+a(n+3)+2*a(n+4)-6*n+18, n >= 10

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) = 52
a \! \left(6\right) = 125
a \! \left(7\right) = 276
a \! \left(8\right) = 581
a \! \left(9\right) = 1184
a \! \left(n +5\right) = -a \! \left(n \right)-2 a \! \left(n +1\right)-a \! \left(n +2\right)+a \! \left(n +3\right)+2 a \! \left(n +4\right)-6 n +18, \quad n \geq 10

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16318/
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[20,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[19,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[18,x]
F[18,x] = F[14,x]
F[19,x] = F[4,x]*F[7,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[13,x]+F[22,x]+F[58,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[24,x]+F[32,x]
F[24,x] = F[25,x]+F[28,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[1,x]+F[25,x]
F[28,x] = F[13,x]+F[14,x]+F[29,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[7,x]
F[31,x] = F[14,x]
F[32,x] = F[33,x]+F[47,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[25,x]+F[31,x]
F[37,x] = F[33,x]+F[38,x]
F[38,x] = F[39,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[4,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[18,x]+F[4,x]
F[45,x] = F[41,x]+F[46,x]
F[46,x] = F[39,x]
F[47,x] = 2*F[13,x]+F[39,x]+F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[53,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[25,x]
F[53,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[54,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[78,x]
F[60,x] = F[2,x]+F[61,x]
F[61,x] = F[13,x]+F[62,x]+F[77,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[12,x]+F[4,x]
F[65,x] = F[41,x]+F[66,x]
F[66,x] = 2*F[13,x]+F[39,x]+F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[72,x]
F[69,x] = F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[25,x]*F[4,x]
F[72,x] = F[73,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[73,x]
F[77,x] = F[2,x]*F[4,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[34,x]
F[80,x] = 2*F[13,x]+F[81,x]+F[87,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[83,x]+F[86,x]
F[83,x] = F[70,x]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[31,x]*F[4,x]
F[86,x] = F[73,x]
F[87,x] = F[4,x]*F[79,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_{20}\! \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_{19}\! \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_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)
F_{19}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{13}\! \left(x \right)+F_{22}\! \left(x \right)+F_{58}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{32}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)+F_{29}\! \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_{7}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{47}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{25}\! \left(x \right)+F_{31}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \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_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{18}\! \left(x \right)+F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = F_{41}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{39}\! \left(x \right)
F_{47}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{39}\! \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_{53}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{25}\! \left(x \right)
F_{53}\! \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_{54}\! \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_{78}\! \left(x \right)
F_{60}\! \left(x \right) = F_{2}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{13}\! \left(x \right)+F_{62}\! \left(x \right)+F_{77}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right)+F_{4}\! \left(x \right)
F_{65}\! \left(x \right) = F_{41}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{39}\! \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_{72}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{72}\! \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_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{70}\! \left(x \right)
F_{76}\! \left(x \right) = F_{73}\! \left(x \right)
F_{77}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{34}\! \left(x \right)
F_{80}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{81}\! \left(x \right)+F_{87}\! \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_{86}\! \left(x \right)
F_{83}\! \left(x \right) = F_{70}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{86}\! \left(x \right) = F_{73}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \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_20(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_19(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_18(x))
Eq(F_18(x), F_14(x))
Eq(F_19(x), F_4(x)*F_7(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_13(x) + F_22(x) + F_58(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_24(x) + F_32(x))
Eq(F_24(x), F_25(x) + F_28(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_1(x) + F_25(x))
Eq(F_28(x), F_13(x) + F_14(x) + F_29(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_7(x))
Eq(F_31(x), F_14(x))
Eq(F_32(x), F_33(x) + F_47(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_25(x) + F_31(x))
Eq(F_37(x), F_33(x) + F_38(x))
Eq(F_38(x), F_39(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_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_18(x) + F_4(x))
Eq(F_45(x), F_41(x) + F_46(x))
Eq(F_46(x), F_39(x))
Eq(F_47(x), 2*F_13(x) + F_39(x) + F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_53(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_25(x))
Eq(F_53(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_54(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_78(x))
Eq(F_60(x), F_2(x) + F_61(x))
Eq(F_61(x), F_13(x) + F_62(x) + F_77(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_12(x) + F_4(x))
Eq(F_65(x), F_41(x) + F_66(x))
Eq(F_66(x), 2*F_13(x) + F_39(x) + F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_72(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_25(x)*F_4(x))
Eq(F_72(x), F_73(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_73(x))
Eq(F_77(x), F_2(x)*F_4(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_34(x))
Eq(F_80(x), 2*F_13(x) + F_81(x) + F_87(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_86(x))
Eq(F_83(x), F_70(x) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_31(x)*F_4(x))
Eq(F_86(x), F_73(x))
Eq(F_87(x), F_4(x)*F_79(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": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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, 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": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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, 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": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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, 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, 0], [0, 1], [0, 1]]}, {"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, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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, 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": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 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3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "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": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", 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[[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, 0], [0, 1], [0, 1]]}, {"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, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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, 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": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [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"}}, {"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], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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, 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