0213_0231_0321_1230_2031
Counting sequence:
1, 1, 2, 6, 19, 58, 171, 492, 1391, 3881, 10717, 29351, 79849, 216038, 581846, 1561072, 4174766, 11133851, 29623442, 78658586, 208495964, 551812683, 1458527031, 3850700142, 10156182076, 26763393611, 70472355702, 185440257961, 487677005214, 1281841706793, 3367730372901, 8844322873927, 23218645068571, 60935768124561, 159877286506072, 419367068230676, 1099783750087874, 2883610351265618, 7559477124440181, 19814417977685102, 51929334203275926, 136079492725595926, 356555350420180177, 934158919082703881, 2447251983671325894, 6410690247812606858, 16792009614271464271, 43982055303597423042, 115193017929179109991, 301687340819228517756, 790079024977651302567, 2069037972423241051301, 5418169908657617727649, 14188110346476363297163, 37152295115130149569121, 97283034782502161171322, 254729959207349957583166, 666983907181651108376176, 1746400915197554386423842, 4572635318281631937573111, 11972473237881402445369814, 31347035183183469701282258, 82073864758534187415243856, 214886723055606907228332467, 562614582191940511110615151, 1473022761391666108015098386, 3856606523993292119671596152, 10097152078659664184228129311, 26435675610051045101135862614, 69211794731556831563828708693, 181204171996750295521280311526, 474411097433025216571626940577, 1242053241981120507491233808321, 3251804704610190288582674997411, 8513491232965753161274940841447, 22288972047115064792233028771601, 58354129420730676383041090405324, 152775054007590981468777464408468, 399974840007709844620709960093106, 1047158317159864483129450888693702, 2741520687886040260892988031874601, 7177451580857741983050770896217226, 18790945256081655357248505545688102, 49195642699265818384785118354892506, 128796583808922129030900863272590769, 337195505806756837486107948384504033, 882793181426583125590496757752636746, 2311191588727390557452016712398905342, 6050799136967569385717499467198770091, 15841246626117698822386124953282194506, 41473035599043107089760547396918299667, 108578080688311580865435192809869274876, 284261719106418731968210357005423053199, 744208268375583567595432176984077814913, 1948365856490494593982004093906773696021, 5100895741657637275191526593033510854447, 13354336340971942120343815608943312932441, 34962148088073452253575664948410518280126, 91532188839276891426928880020928672370742, 239634606536701650940127827962818163611136, 627372068066419657726849505558187042211414
Generating function in Maple syntax:
-(2*x^4-4*x^3+8*x^2-5*x+1)/(x^2-3*x+1)/(x^3-2*x^2+3*x-1)
Generating function in latex syntax:
-\frac{2 x^{4}-4 x^{3}+8 x^{2}-5 x +1}{\left(x^{2}-3 x +1\right) \left(x^{3}-2 x^{2}+3 x -1\right)}
Generating function in sympy syntax:
(-2*x**4 + 4*x**3 - 8*x**2 + 5*x - 1)/((x**2 - 3*x + 1)*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(x^3-2*x^2+3*x-1)*F(x)+2*x^4-4*x^3+8*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(x^{3}-2 x^{2}+3 x -1\right) F \! \left(x \right)+2 x^{4}-4 x^{3}+8 x^{2}-5 x +1 = 0
Explicit closed form in Maple syntax:
11/60000*((7/3*((I+96/161*23^(1/2))*3^(1/2)-134/161*I*23^(1/2)+1/7)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)-65/6*2^(2/3)*((I-45/299*23^(1/2))*3^(1/2)-1/299*I*23^(1/2)+35/13)*(11+3*23^(1/2)*3^(1/2))^(1/3)+50/3+2150/69*I*23^(1/2))*(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)+(((I+19/69*23^(1/2))*3^(1/2)-11/3-211/69*I*23^(1/2))*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)-20*2^(2/3)*((I+11/276*23^(1/2))*3^(1/2)-17/138*I*23^(1/2)+1/12)*(11+3*23^(1/2)*3^(1/2))^(1/3)+50/3-2150/69*I*23^(1/2))*(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)+(-10/3*((I+1/2*23^(1/2))*3^(1/2)-3/2*I*23^(1/2)-1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+200/3+185/6*2^(2/3)*((I-1/37*23^(1/2))*3^(1/2)-3/37*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(1/3))*(3/2-1/2*5^(1/2))^(-n)+(-10/3*((I+1/2*23^(1/2))*3^(1/2)-3/2*I*23^(1/2)-1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+200/3+185/6*2^(2/3)*((I-1/37*23^(1/2))*3^(1/2)-3/37*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(1/3))*(3/2+1/2*5^(1/2))^(-n)-100*(-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))*(((I+19/253*23^(1/2))*3^(1/2)-57/253*I*23^(1/2)-1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+200/11-5/11*2^(2/3)*((I+11/23*23^(1/2))*3^(1/2)+33/23*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(1/3))
Explicit closed form in latex syntax:
\frac{11 \left(\left(\frac{7 \left(\left(\mathrm{I}+\frac{96 \sqrt{23}}{161}\right) \sqrt{3}-\frac{134 \,\mathrm{I} \sqrt{23}}{161}+\frac{1}{7}\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{3}-\frac{65 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}-\frac{45 \sqrt{23}}{299}\right) \sqrt{3}-\frac{\mathrm{I} \sqrt{23}}{299}+\frac{35}{13}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{50}{3}+\frac{2150 \,\mathrm{I} \sqrt{23}}{69}\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}+\left(\left(\left(\mathrm{I}+\frac{19 \sqrt{23}}{69}\right) \sqrt{3}-\frac{11}{3}-\frac{211 \,\mathrm{I} \sqrt{23}}{69}\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}-20 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}+\frac{11 \sqrt{23}}{276}\right) \sqrt{3}-\frac{17 \,\mathrm{I} \sqrt{23}}{138}+\frac{1}{12}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+\frac{50}{3}-\frac{2150 \,\mathrm{I} \sqrt{23}}{69}\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}+\left(-\frac{10 \left(\left(\mathrm{I}+\frac{\sqrt{23}}{2}\right) \sqrt{3}-\frac{3 \,\mathrm{I} \sqrt{23}}{2}-1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{3}+\frac{200}{3}+\frac{185 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}-\frac{\sqrt{23}}{37}\right) \sqrt{3}-\frac{3 \,\mathrm{I} \sqrt{23}}{37}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}+\left(-\frac{10 \left(\left(\mathrm{I}+\frac{\sqrt{23}}{2}\right) \sqrt{3}-\frac{3 \,\mathrm{I} \sqrt{23}}{2}-1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{3}+\frac{200}{3}+\frac{185 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}-\frac{\sqrt{23}}{37}\right) \sqrt{3}-\frac{3 \,\mathrm{I} \sqrt{23}}{37}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}-100 \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}\right) \left(\left(\left(\mathrm{I}+\frac{19 \sqrt{23}}{253}\right) \sqrt{3}-\frac{57 \,\mathrm{I} \sqrt{23}}{253}-1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+\frac{200}{11}-\frac{5 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}+\frac{11 \sqrt{23}}{23}\right) \sqrt{3}+\frac{33 \,\mathrm{I} \sqrt{23}}{23}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{11}\right)}{60000}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n+5) = a(n)-5*a(n+1)+10*a(n+2)-12*a(n+3)+6*a(n+4), n >= 5
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(n +5\right) = a \! \left(n \right)-5 a \! \left(n +1\right)+10 a \! \left(n +2\right)-12 a \! \left(n +3\right)+6 a \! \left(n +4\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://www.permpal.com/tree/20256/
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[10,x]*F[4,x]
F[4,x] = F[14,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[10,x]*F[8,x]
F[8,x] = F[5,x]+F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = x
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[13,x]
F[13,x] = F[9,x]
F[14,x] = F[15,x]+F[43,x]
F[15,x] = F[16,x]
F[16,x] = F[10,x]*F[17,x]
F[17,x] = F[18,x]+F[22,x]
F[18,x] = F[1,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[10,x]*F[21,x]
F[21,x] = F[1,x]+F[10,x]
F[22,x] = F[15,x]+F[23,x]
F[23,x] = F[24,x]+F[25,x]+F[41,x]
F[24,x] = 0
F[25,x] = F[10,x]*F[26,x]
F[26,x] = F[27,x]+F[31,x]
F[27,x] = F[19,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[10,x]*F[30,x]
F[30,x] = F[10,x]
F[31,x] = F[23,x]+F[32,x]
F[32,x] = 2*F[24,x]+F[33,x]+F[37,x]
F[33,x] = F[10,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[28,x]
F[36,x] = F[32,x]
F[37,x] = F[10,x]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[10,x]*F[15,x]
F[41,x] = F[10,x]*F[42,x]
F[42,x] = F[15,x]+F[39,x]
F[43,x] = F[24,x]+F[44,x]+F[73,x]
F[44,x] = F[10,x]*F[45,x]
F[45,x] = F[46,x]+F[50,x]
F[46,x] = F[47,x]+F[6,x]
F[47,x] = F[12,x]+F[24,x]+F[48,x]
F[48,x] = F[10,x]*F[49,x]
F[49,x] = F[11,x]+F[6,x]
F[50,x] = F[43,x]+F[51,x]
F[51,x] = F[24,x]+F[52,x]+F[67,x]+F[71,x]
F[52,x] = F[10,x]*F[53,x]
F[53,x] = F[54,x]+F[58,x]
F[54,x] = F[47,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[10,x]*F[57,x]
F[57,x] = F[11,x]
F[58,x] = F[51,x]+F[59,x]
F[59,x] = 2*F[24,x]+F[60,x]+F[64,x]+F[70,x]
F[60,x] = F[10,x]*F[61,x]
F[61,x] = F[62,x]+F[63,x]
F[62,x] = F[55,x]
F[63,x] = F[59,x]
F[64,x] = F[10,x]*F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[10,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[39,x]+F[66,x]
F[70,x] = 0
F[71,x] = F[10,x]*F[72,x]
F[72,x] = F[43,x]+F[66,x]
F[73,x] = F[10,x]*F[74,x]
F[74,x] = F[14,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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{14}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{10}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{5}\! \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) = x
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{43}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{10}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \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_{25}\! \left(x \right)+F_{41}\! \left(x \right)
F_{24}\! \left(x \right) = 0
F_{25}\! \left(x \right) = F_{10}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{31}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{10}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{10}\! \left(x \right)
F_{31}\! \left(x \right) = F_{23}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{33}\! \left(x \right)+F_{37}\! \left(x \right)
F_{33}\! \left(x \right) = F_{10}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{28}\! \left(x \right)
F_{36}\! \left(x \right) = F_{32}\! \left(x \right)
F_{37}\! \left(x \right) = F_{10}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{10}\! \left(x \right) F_{15}\! \left(x \right)
F_{41}\! \left(x \right) = F_{10}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right)+F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{24}\! \left(x \right)+F_{44}\! \left(x \right)+F_{73}\! \left(x \right)
F_{44}\! \left(x \right) = F_{10}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{50}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{6}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right)+F_{24}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right)+F_{6}\! \left(x \right)
F_{50}\! \left(x \right) = F_{43}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{24}\! \left(x \right)+F_{52}\! \left(x \right)+F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{52}\! \left(x \right) = F_{10}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{58}\! \left(x \right)
F_{54}\! \left(x \right) = F_{47}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{10}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right)
F_{58}\! \left(x \right) = F_{51}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{60}\! \left(x \right)+F_{64}\! \left(x \right)+F_{70}\! \left(x \right)
F_{60}\! \left(x \right) = F_{10}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{55}\! \left(x \right)
F_{63}\! \left(x \right) = F_{59}\! \left(x \right)
F_{64}\! \left(x \right) = F_{10}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{10}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{39}\! \left(x \right)+F_{66}\! \left(x \right)
F_{70}\! \left(x \right) = 0
F_{71}\! \left(x \right) = F_{10}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{43}\! \left(x \right)+F_{66}\! \left(x \right)
F_{73}\! \left(x \right) = F_{10}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{14}\! \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_10(x)*F_4(x))
Eq(F_4(x), F_14(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_10(x)*F_8(x))
Eq(F_8(x), F_5(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), x)
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_13(x))
Eq(F_13(x), F_9(x))
Eq(F_14(x), F_15(x) + F_43(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_10(x)*F_17(x))
Eq(F_17(x), F_18(x) + F_22(x))
Eq(F_18(x), F_1(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_10(x)*F_21(x))
Eq(F_21(x), F_1(x) + F_10(x))
Eq(F_22(x), F_15(x) + F_23(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_41(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_10(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_31(x))
Eq(F_27(x), F_19(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_10(x)*F_30(x))
Eq(F_30(x), F_10(x))
Eq(F_31(x), F_23(x) + F_32(x))
Eq(F_32(x), 2*F_24(x) + F_33(x) + F_37(x))
Eq(F_33(x), F_10(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_28(x))
Eq(F_36(x), F_32(x))
Eq(F_37(x), F_10(x)*F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_10(x)*F_15(x))
Eq(F_41(x), F_10(x)*F_42(x))
Eq(F_42(x), F_15(x) + F_39(x))
Eq(F_43(x), F_24(x) + F_44(x) + F_73(x))
Eq(F_44(x), F_10(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_50(x))
Eq(F_46(x), F_47(x) + F_6(x))
Eq(F_47(x), F_12(x) + F_24(x) + F_48(x))
Eq(F_48(x), F_10(x)*F_49(x))
Eq(F_49(x), F_11(x) + F_6(x))
Eq(F_50(x), F_43(x) + F_51(x))
Eq(F_51(x), F_24(x) + F_52(x) + F_67(x) + F_71(x))
Eq(F_52(x), F_10(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_58(x))
Eq(F_54(x), F_47(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_10(x)*F_57(x))
Eq(F_57(x), F_11(x))
Eq(F_58(x), F_51(x) + F_59(x))
Eq(F_59(x), 2*F_24(x) + F_60(x) + F_64(x) + F_70(x))
Eq(F_60(x), F_10(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_63(x))
Eq(F_62(x), F_55(x))
Eq(F_63(x), F_59(x))
Eq(F_64(x), F_10(x)*F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_10(x)*F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_39(x) + F_66(x))
Eq(F_70(x), 0)
Eq(F_71(x), F_10(x)*F_72(x))
Eq(F_72(x), F_43(x) + F_66(x))
Eq(F_73(x), F_10(x)*F_74(x))
Eq(F_74(x), F_14(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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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, 2, 1, 3], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": []}, {"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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], 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