0132_0213_0231_2130_3102
Counting sequence:
1, 1, 2, 6, 19, 52, 123, 270, 576, 1226, 2637, 5755, 12735, 28501, 64331, 146108, 333335, 763007, 1750936, 4025973, 9271848, 21381475, 49362217, 114068527, 263810878, 610557000, 1413919300, 3276061434, 7594120132, 17610596373, 40852494680, 94796186176, 220025721729, 510800407354, 1186072212753, 2754494050412, 6397843153486, 14862023624344, 34527698732619, 80222532348329, 186405503710037, 433161706193843, 1006621765582569, 2339397632234306, 5437011560080309, 12636662158074037, 29370962939757558, 68267779970153635, 158680484002944326, 368841670636161241, 857361455128535647, 1992940770627835765, 4632659597285846500, 10768895755776939726, 25033182943480074146, 58192165116358456368, 135274521618264739370, 314463410366302584947, 731015338580227193886, 1699357687829322127438, 3950433739099776588583, 9183457065032836782560, 21348573174352127516407, 49628662671338182075802, 115371145808838521053068, 268202379415182112749110, 623488897613189050744185, 1449423856446004592922599, 3369477706782744080383707, 7833037411581264686849313, 18209506890648015654394615, 42331775981611671993349336, 98409056427215070005170819, 228772533913259522977440379, 531830084275339383503904068, 1236351880243472739739268897, 2874163283726516105542093396, 6681606730234976481361081759, 15532826614029438494157329669, 36109391886413015668130060619, 83944053603551420583113030522, 195146052536130217078589301028, 453659140056245922080378059184, 1054628764237118945352481079606, 2451712856209175594346101535424, 5699537762357895585155370907297, 13249811503189176053609691712468, 30802062169654355667831037008300, 71606081922129496647362303000701, 166463894244642726991900935885206, 386981503688071088012542057244557, 899622649754552396028652240343000, 2091368526647147917707704817405690, 4861841165150390406388214578967076, 11302407853971388494397611443053911, 26274907282380454017363560190121653, 61081742352588818328162572666455505, 141997810443456621161116009868902687, 330104834100532052278302046077641461, 767400584153190475708667894389300478, 1783989815473801429466178007337262593
Generating function in Maple syntax:
-(4*x^10-12*x^9+16*x^8-5*x^7-22*x^6+41*x^5-53*x^4+49*x^3-27*x^2+8*x-1)/(2*x-1)/(x^3-2*x^2+3*x-1)/(-1+x)^4
Generating function in latex syntax:
-\frac{4 x^{10}-12 x^{9}+16 x^{8}-5 x^{7}-22 x^{6}+41 x^{5}-53 x^{4}+49 x^{3}-27 x^{2}+8 x -1}{\left(2 x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(-1+x \right)^{4}}
Generating function in sympy syntax:
(-4*x**10 + 12*x**9 - 16*x**8 + 5*x**7 + 22*x**6 - 41*x**5 + 53*x**4 - 49*x**3 + 27*x**2 - 8*x + 1)/((x - 1)**4*(2*x - 1)*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^3-2*x^2+3*x-1)*(-1+x)^4*F(x)+4*x^10-12*x^9+16*x^8-5*x^7-22*x^6+41*x^5-53*x^4+49*x^3-27*x^2+8*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(-1+x \right)^{4} F \! \left(x \right)+4 x^{10}-12 x^{9}+16 x^{8}-5 x^{7}-22 x^{6}+41 x^{5}-53 x^{4}+49 x^{3}-27 x^{2}+8 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,n = 2,2,1/13800*(-46*2^(1/3)*((-4/23*23^(1/2)+I)*3^(1/2)-12/23*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(2/3)+4600+115*((-1/23*23^(1/2)+I)*3^(1/2)+3/23*I*23^(1/2)-1)*2^(2/3)*(11+3*23^(1/2)*3^(1/2))^(1/3))*(11/600*2^(1/3)*((I-3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)+1)*(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*(-115*2^(2/3)*((1/23*23^(1/2)+I)*3^(1/2)+3/23*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(1/3)+4600+46*2^(1/3)*((4/23*23^(1/2)+I)*3^(1/2)-12/23*I*23^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(2/3))*(-11/600*2^(1/3)*((I+3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)-1)*(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*((10*23^(1/2)*2^(2/3)*3^(1/2)+230*2^(2/3))*(11+3*23^(1/2)*3^(1/2))^(1/3)+4600+(-16*23^(1/2)*3^(1/2)*2^(1/3)+92*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)+1/3*n^3-1/2*n^2-41/6*n+2^(-1+n)+13)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ 2 & n =2 \\ \frac{\left(-46 \,2^{\frac{1}{3}} \left(\left(-\frac{4 \sqrt{23}}{23}+\mathrm{I}\right) \sqrt{3}-\frac{12 \,\mathrm{I} \sqrt{23}}{23}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+4600+115 \left(\left(-\frac{\sqrt{23}}{23}+\mathrm{I}\right) \sqrt{3}+\frac{3 \,\mathrm{I} \sqrt{23}}{23}-1\right) 2^{\frac{2}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{11 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}+1\right) \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(-115 \,2^{\frac{2}{3}} \left(\left(\frac{\sqrt{23}}{23}+\mathrm{I}\right) \sqrt{3}+\frac{3 \,\mathrm{I} \sqrt{23}}{23}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+4600+46 \,2^{\frac{1}{3}} \left(\left(\frac{4 \sqrt{23}}{23}+\mathrm{I}\right) \sqrt{3}-\frac{12 \,\mathrm{I} \sqrt{23}}{23}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{11 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}-1\right) \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(10 \sqrt{23}\, 2^{\frac{2}{3}} \sqrt{3}+230 \,2^{\frac{2}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+4600+\left(-16 \sqrt{23}\, \sqrt{3}\, 2^{\frac{1}{3}}+92 \,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{n^{3}}{3}-\frac{n^{2}}{2}-\frac{41 n}{6}+2^{-1+n}+13 & \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) = 123
a(7) = 270
a(8) = 576
a(9) = 1226
a(10) = 2637
a(n+4) = -2*a(n)+5*a(n+1)-8*a(n+2)+5*a(n+3)+1/6*(n+5)*(2*n^2-13*n+12), n >= 11
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) = 123
a \! \left(7\right) = 270
a \! \left(8\right) = 576
a \! \left(9\right) = 1226
a \! \left(10\right) = 2637
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)+\frac{\left(n +5\right) \left(2 n^{2}-13 n +12\right)}{6}, \quad n \geq 11
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18211/
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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[7,x]
F[14,x] = F[15,x]+F[26,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[6,x]
F[18,x] = F[15,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[15,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[22,x]*F[4,x]
F[25,x] = F[19,x]
F[26,x] = F[27,x]+F[28,x]+F[61,x]
F[27,x] = 0
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[40,x]
F[30,x] = F[31,x]+F[7,x]
F[31,x] = F[27,x]+F[32,x]+F[37,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]
F[34,x] = F[11,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[34,x]*F[4,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[13,x]+F[39,x]
F[39,x] = F[31,x]
F[40,x] = F[41,x]+F[60,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[46,x]
F[44,x] = F[45,x]+F[7,x]
F[45,x] = F[32,x]
F[46,x] = F[41,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[51,x]+F[58,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[56,x]
F[54,x] = F[11,x]+F[55,x]
F[55,x] = F[32,x]
F[56,x] = F[51,x]+F[57,x]
F[57,x] = F[48,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[50,x]
F[60,x] = F[48,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]+F[73,x]
F[63,x] = F[15,x]+F[64,x]
F[64,x] = F[27,x]+F[65,x]+F[72,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[70,x]
F[67,x] = F[11,x]+F[68,x]
F[68,x] = F[27,x]+F[32,x]+F[69,x]
F[69,x] = F[13,x]*F[4,x]
F[70,x] = F[51,x]+F[71,x]
F[71,x] = F[48,x]
F[72,x] = F[4,x]*F[63,x]
F[73,x] = F[74,x]
F[74,x] = F[27,x]+F[75,x]+F[77,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[30,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[22,x]+F[79,x]
F[79,x] = F[74,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_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{6}\! \left(x \right)
F_{18}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{19}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{61}\! \left(x \right)
F_{27}\! \left(x \right) = 0
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_{40}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{7}\! \left(x \right)
F_{31}\! \left(x \right) = F_{27}\! \left(x \right)+F_{32}\! \left(x \right)+F_{37}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{13}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{31}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{60}\! \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_{46}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{7}\! \left(x \right)
F_{45}\! \left(x \right) = F_{32}\! \left(x \right)
F_{46}\! \left(x \right) = F_{41}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{58}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{11}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{32}\! \left(x \right)
F_{56}\! \left(x \right) = F_{51}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{48}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{60}\! \left(x \right) = F_{48}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{73}\! \left(x \right)
F_{63}\! \left(x \right) = F_{15}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{27}\! \left(x \right)+F_{65}\! \left(x \right)+F_{72}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{70}\! \left(x \right)
F_{67}\! \left(x \right) = F_{11}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{27}\! \left(x \right)+F_{32}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{70}\! \left(x \right) = F_{51}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{48}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{27}\! \left(x \right)+F_{75}\! \left(x \right)+F_{77}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{30}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{22}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{74}\! \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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_7(x))
Eq(F_14(x), F_15(x) + F_26(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_6(x))
Eq(F_18(x), F_15(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_15(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_22(x)*F_4(x))
Eq(F_25(x), F_19(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_61(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_40(x))
Eq(F_30(x), F_31(x) + F_7(x))
Eq(F_31(x), F_27(x) + F_32(x) + F_37(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_11(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_34(x)*F_4(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_13(x) + F_39(x))
Eq(F_39(x), F_31(x))
Eq(F_40(x), F_41(x) + F_60(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_46(x))
Eq(F_44(x), F_45(x) + F_7(x))
Eq(F_45(x), F_32(x))
Eq(F_46(x), F_41(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_51(x) + F_58(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_56(x))
Eq(F_54(x), F_11(x) + F_55(x))
Eq(F_55(x), F_32(x))
Eq(F_56(x), F_51(x) + F_57(x))
Eq(F_57(x), F_48(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_50(x))
Eq(F_60(x), F_48(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_73(x))
Eq(F_63(x), F_15(x) + F_64(x))
Eq(F_64(x), F_27(x) + F_65(x) + F_72(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_70(x))
Eq(F_67(x), F_11(x) + F_68(x))
Eq(F_68(x), F_27(x) + F_32(x) + F_69(x))
Eq(F_69(x), F_13(x)*F_4(x))
Eq(F_70(x), F_51(x) + F_71(x))
Eq(F_71(x), F_48(x))
Eq(F_72(x), F_4(x)*F_63(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_27(x) + F_75(x) + F_77(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_30(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_22(x) + F_79(x))
Eq(F_79(x), F_74(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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3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, 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"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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [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, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}], "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": 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