0123_0213_0231_2130
Counting sequence:
1, 1, 2, 6, 20, 65, 197, 556, 1481, 3780, 9362, 22713, 54338, 128780, 303290, 711275, 1663376, 3882565, 9050872, 21080683, 49070654, 114178194, 265597371, 617705175, 1436419562, 3339963147, 7765591223, 18054617422, 41974816064, 97584334558, 226863697936, 527406475027, 1226091301705, 2850348819237, 6626309426816, 15404385199941, 35810987910879, 83250668352093, 193534682362291, 449914131802757, 1045924400460561, 2431480755059041, 5652509432389512, 13140494158746456, 30547949174068325, 71015376415867265, 165090737644506027, 383789429640890196, 892202223000835076, 2074118600681553235, 4821740871951484332, 11209187777076079563, 26058200413858294793, 60577966924809545960, 140826688315074900445, 327382332466185975555, 761071589241226475661, 1769276793611113209090, 4113069538869812243107, 9561726625185907163388, 22228317602039420130639, 51674569111783938548934, 120128798784236772650681, 279265575776127431267625, 649213698944416147372142, 1509238744182899382770122, 3508554410626385775623953, 8156399442765836229958962, 18961328251726090533367534, 44079740281079500448951413, 102472963783857126055104531, 238220739043249952878858577, 553796029846531561598331635, 1287419575242479844793378642, 2992887405086570758386239196, 6957619094635756481195089696, 16174502049000024499954763739, 37601155362853020358233626968, 87412081085256074346708192226, 203208434579161401676706985112, 472402296929985577338754713846, 1098202102717149698506469640956, 2553010148871059538659334130872, 5935028538109544687941456603956, 13797267419304764772790537466555, 32074755330568044460564038216915, 74564759691207028591246867324532, 173342035831794421672013438730336, 402971343443544792407915366306046, 936794718358264762631381210866715, 2177783504019518865024546207156927, 5062732418785603802653426556366238, 11769424966676090121251423324205323, 27360593566476665244615452915701990, 63605663184863554595849283362054300, 147865227388313642342564202134388235, 343744949361690837305457671856936596, 799110056493309354974937908481443790, 1857705498144860960029154776944126492, 4318641330809656507963582392622801693, 10039623052632559386700603932436977474
Generating function in Maple syntax:
-(2*x^8-4*x^7+8*x^6+2*x^5-20*x^4+28*x^3-20*x^2+7*x-1)/(x^2+x-1)/(x^3-2*x^2+3*x-1)/(x-1)^4
Generating function in latex syntax:
-\frac{2 x^{8}-4 x^{7}+8 x^{6}+2 x^{5}-20 x^{4}+28 x^{3}-20 x^{2}+7 x -1}{\left(x^{2}+x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-2*x**8 + 4*x**7 - 8*x**6 - 2*x**5 + 20*x**4 - 28*x**3 + 20*x**2 - 7*x + 1)/((x - 1)**4*(x**2 + x - 1)*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^2+x-1)*(x^3-2*x^2+3*x-1)*(x-1)^4*F(x)+2*x^8-4*x^7+8*x^6+2*x^5-20*x^4+28*x^3-20*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}+x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{4} F \! \left(x \right)+2 x^{8}-4 x^{7}+8 x^{6}+2 x^{5}-20 x^{4}+28 x^{3}-20 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
1/34500*(-1265*2^(2/3)*((-177/253*I+59/253*3^(1/2))*23^(1/2)+I*3^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(1/3)+39100-943*((33/943*I+11/943*3^(1/2))*23^(1/2)+I*3^(1/2)+1)*2^(1/3)*(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)+1/34500*(1265*((-177/253*I-59/253*3^(1/2))*23^(1/2)+I*3^(1/2)+1)*2^(2/3)*(11+3*23^(1/2)*3^(1/2))^(1/3)+39100+943*((33/943*I-11/943*3^(1/2))*23^(1/2)+I*3^(1/2)-1)*2^(1/3)*(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)+1/34500*((590*2^(2/3)*23^(1/2)*3^(1/2)-2530*2^(2/3))*(11+3*23^(1/2)*3^(1/2))^(1/3)+39100+(22*23^(1/2)*3^(1/2)*2^(1/3)+1886*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)+1/34500*(72450*5^(1/2)-162150)*(-1/2*5^(1/2)-1/2)^(-n)+1/34500*(-72450*5^(1/2)-162150)*(1/2*5^(1/2)-1/2)^(-n)-1/3*n^3+3/2*n^2+11/6*n+7
Explicit closed form in latex syntax:
\frac{\left(-1265 \,2^{\frac{2}{3}} \left(\left(-\frac{177 \,\mathrm{I}}{253}+\frac{59 \sqrt{3}}{253}\right) \sqrt{23}+\mathrm{I} \sqrt{3}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+39100-943 \left(\left(\frac{33 \,\mathrm{I}}{943}+\frac{11 \sqrt{3}}{943}\right) \sqrt{23}+\mathrm{I} \sqrt{3}+1\right) 2^{\frac{1}{3}} \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}}{34500}+\frac{\left(1265 \left(\left(-\frac{177 \,\mathrm{I}}{253}-\frac{59 \sqrt{3}}{253}\right) \sqrt{23}+\mathrm{I} \sqrt{3}+1\right) 2^{\frac{2}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+39100+943 \left(\left(\frac{33 \,\mathrm{I}}{943}-\frac{11 \sqrt{3}}{943}\right) \sqrt{23}+\mathrm{I} \sqrt{3}-1\right) 2^{\frac{1}{3}} \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}}{34500}+\frac{\left(\left(590 \,2^{\frac{2}{3}} \sqrt{23}\, \sqrt{3}-2530 \,2^{\frac{2}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+39100+\left(22 \sqrt{23}\, \sqrt{3}\, 2^{\frac{1}{3}}+1886 \,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}}{34500}+\frac{\left(72450 \sqrt{5}-162150\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{34500}+\frac{\left(-72450 \sqrt{5}-162150\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{34500}-\frac{n^{3}}{3}+\frac{3 n^{2}}{2}+\frac{11 n}{6}+7
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 65
a(6) = 197
a(7) = 556
a(8) = 1481
a(n+1) = 1/3*n^3-3/2*n^2+4*a(n+3)-4*a(n+4)+a(n+5)+a(n)-35/6*n-9, n >= 9
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) = 65
a \! \left(6\right) = 197
a \! \left(7\right) = 556
a \! \left(8\right) = 1481
a \! \left(n +1\right) = \frac{n^{3}}{3}-\frac{3 n^{2}}{2}+4 a \! \left(n +3\right)-4 a \! \left(n +4\right)+a \! \left(n +5\right)+a \! \left(n \right)-\frac{35 n}{6}-9, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14900/
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[2,x]
F[15,x] = F[136,x]+F[16,x]+F[17,x]
F[16,x] = 0
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]+F[30,x]
F[19,x] = F[20,x]+F[7,x]
F[20,x] = F[16,x]+F[21,x]+F[27,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]
F[23,x] = F[11,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[11,x]+F[24,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[13,x]+F[29,x]
F[29,x] = F[20,x]
F[30,x] = F[31,x]+F[65,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[38,x]
F[34,x] = F[35,x]+F[7,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[11,x]
F[38,x] = F[31,x]+F[39,x]
F[39,x] = 2*F[16,x]+F[40,x]+F[48,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[35,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[35,x]
F[47,x] = F[44,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]+F[55,x]
F[53,x] = F[11,x]+F[54,x]
F[54,x] = F[36,x]
F[55,x] = F[50,x]+F[56,x]
F[56,x] = 2*F[16,x]+F[48,x]+F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[54,x]
F[60,x] = F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[54,x]
F[64,x] = F[61,x]
F[65,x] = 2*F[16,x]+F[118,x]+F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[72,x]
F[68,x] = F[20,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[24,x]
F[72,x] = F[107,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[80,x]
F[76,x] = F[20,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[24,x]
F[80,x] = F[73,x]+F[81,x]
F[81,x] = 3*F[16,x]+F[82,x]+F[90,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[77,x]
F[85,x] = F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[77,x]
F[89,x] = F[86,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[95,x]+F[97,x]
F[95,x] = F[24,x]+F[96,x]
F[96,x] = F[78,x]
F[97,x] = F[92,x]+F[98,x]
F[98,x] = 3*F[16,x]+F[90,x]+F[99,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[96,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]+F[106,x]
F[105,x] = F[96,x]
F[106,x] = F[103,x]
F[107,x] = 3*F[16,x]+F[108,x]+F[116,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[69,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[69,x]
F[115,x] = F[112,x]
F[116,x] = F[117,x]*F[4,x]
F[117,x] = F[92,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]+F[50,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[124,x]+F[126,x]
F[124,x] = F[125,x]+F[24,x]
F[125,x] = F[70,x]
F[126,x] = F[127,x]+F[92,x]
F[127,x] = 3*F[16,x]+F[116,x]+F[128,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[130,x]+F[131,x]
F[130,x] = F[125,x]
F[131,x] = F[132,x]
F[132,x] = F[133,x]*F[4,x]
F[133,x] = F[134,x]+F[135,x]
F[134,x] = F[125,x]
F[135,x] = F[132,x]
F[136,x] = F[137,x]*F[4,x]
F[137,x] = F[138,x]+F[178,x]
F[138,x] = F[139,x]+F[2,x]
F[139,x] = F[140,x]+F[16,x]+F[177,x]
F[140,x] = F[141,x]*F[4,x]
F[141,x] = F[142,x]+F[146,x]
F[142,x] = F[11,x]+F[143,x]
F[143,x] = F[144,x]+F[16,x]+F[21,x]
F[144,x] = F[145,x]*F[4,x]
F[145,x] = F[143,x]+F[7,x]
F[146,x] = F[147,x]+F[50,x]
F[147,x] = 2*F[16,x]+F[118,x]+F[148,x]
F[148,x] = F[149,x]*F[4,x]
F[149,x] = F[150,x]+F[152,x]
F[150,x] = F[143,x]+F[151,x]
F[151,x] = F[70,x]
F[152,x] = F[153,x]+F[168,x]
F[153,x] = F[154,x]
F[154,x] = F[155,x]*F[4,x]
F[155,x] = F[156,x]+F[158,x]
F[156,x] = F[143,x]+F[157,x]
F[157,x] = F[78,x]
F[158,x] = F[153,x]+F[159,x]
F[159,x] = 3*F[16,x]+F[160,x]+F[90,x]
F[160,x] = F[161,x]*F[4,x]
F[161,x] = F[162,x]+F[163,x]
F[162,x] = F[157,x]
F[163,x] = F[164,x]
F[164,x] = F[165,x]*F[4,x]
F[165,x] = F[166,x]+F[167,x]
F[166,x] = F[157,x]
F[167,x] = F[164,x]
F[168,x] = 3*F[16,x]+F[116,x]+F[169,x]
F[169,x] = F[170,x]*F[4,x]
F[170,x] = F[171,x]+F[172,x]
F[171,x] = F[151,x]
F[172,x] = F[173,x]
F[173,x] = F[174,x]*F[4,x]
F[174,x] = F[175,x]+F[176,x]
F[175,x] = F[151,x]
F[176,x] = F[173,x]
F[177,x] = F[138,x]*F[4,x]
F[178,x] = F[15,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_{2}\! \left(x \right)
F_{15}\! \left(x \right) = F_{136}\! \left(x \right)+F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = 0
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{30}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{7}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right)+F_{21}\! \left(x \right)+F_{27}\! \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_{23}\! \left(x \right) = F_{11}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)+F_{24}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{20}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{65}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \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_{38}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{7}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right)
F_{38}\! \left(x \right) = F_{31}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{40}\! \left(x \right)+F_{48}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{35}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{35}\! \left(x \right)
F_{47}\! \left(x \right) = F_{44}\! \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_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{36}\! \left(x \right)
F_{55}\! \left(x \right) = F_{50}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{48}\! \left(x \right)+F_{57}\! \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_{54}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \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_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{54}\! \left(x \right)
F_{64}\! \left(x \right) = F_{61}\! \left(x \right)
F_{65}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{118}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{72}\! \left(x \right)
F_{68}\! \left(x \right) = F_{20}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{24}\! \left(x \right)
F_{72}\! \left(x \right) = F_{107}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{76}\! \left(x \right) = F_{20}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{24}\! \left(x \right)
F_{80}\! \left(x \right) = F_{73}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{82}\! \left(x \right)+F_{90}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{77}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{77}\! \left(x \right)
F_{89}\! \left(x \right) = F_{86}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{97}\! \left(x \right)
F_{95}\! \left(x \right) = F_{24}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{78}\! \left(x \right)
F_{97}\! \left(x \right) = F_{92}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{90}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{96}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{96}\! \left(x \right)
F_{106}\! \left(x \right) = F_{103}\! \left(x \right)
F_{107}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{108}\! \left(x \right)+F_{116}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{69}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{69}\! \left(x \right)
F_{115}\! \left(x \right) = F_{112}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{92}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{50}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{4}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{126}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{24}\! \left(x \right)
F_{125}\! \left(x \right) = F_{70}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{92}\! \left(x \right)
F_{127}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{116}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{131}\! \left(x \right)
F_{130}\! \left(x \right) = F_{125}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{135}\! \left(x \right)
F_{134}\! \left(x \right) = F_{125}\! \left(x \right)
F_{135}\! \left(x \right) = F_{132}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{178}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{2}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{16}\! \left(x \right)+F_{177}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{146}\! \left(x \right)
F_{142}\! \left(x \right) = F_{11}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{16}\! \left(x \right)+F_{21}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{4}\! \left(x \right)
F_{145}\! \left(x \right) = F_{143}\! \left(x \right)+F_{7}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{50}\! \left(x \right)
F_{147}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{118}\! \left(x \right)+F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{4}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{152}\! \left(x \right)
F_{150}\! \left(x \right) = F_{143}\! \left(x \right)+F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{70}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{168}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right) F_{4}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{158}\! \left(x \right)
F_{156}\! \left(x \right) = F_{143}\! \left(x \right)+F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{78}\! \left(x \right)
F_{158}\! \left(x \right) = F_{153}\! \left(x \right)+F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{160}\! \left(x \right)+F_{90}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right) F_{4}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{163}\! \left(x \right)
F_{162}\! \left(x \right) = F_{157}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right) F_{4}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{167}\! \left(x \right)
F_{166}\! \left(x \right) = F_{157}\! \left(x \right)
F_{167}\! \left(x \right) = F_{164}\! \left(x \right)
F_{168}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{116}\! \left(x \right)+F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right) F_{4}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)+F_{172}\! \left(x \right)
F_{171}\! \left(x \right) = F_{151}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right) F_{4}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{176}\! \left(x \right)
F_{175}\! \left(x \right) = F_{151}\! \left(x \right)
F_{176}\! \left(x \right) = F_{173}\! \left(x \right)
F_{177}\! \left(x \right) = F_{138}\! \left(x \right) F_{4}\! \left(x \right)
F_{178}\! \left(x \right) = F_{15}\! \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_2(x))
Eq(F_15(x), F_136(x) + F_16(x) + F_17(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x) + F_30(x))
Eq(F_19(x), F_20(x) + F_7(x))
Eq(F_20(x), F_16(x) + F_21(x) + F_27(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_11(x) + F_24(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_13(x) + F_29(x))
Eq(F_29(x), F_20(x))
Eq(F_30(x), F_31(x) + F_65(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_38(x))
Eq(F_34(x), F_35(x) + F_7(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_11(x))
Eq(F_38(x), F_31(x) + F_39(x))
Eq(F_39(x), 2*F_16(x) + F_40(x) + F_48(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_35(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_35(x))
Eq(F_47(x), F_44(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))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_55(x))
Eq(F_53(x), F_11(x) + F_54(x))
Eq(F_54(x), F_36(x))
Eq(F_55(x), F_50(x) + F_56(x))
Eq(F_56(x), 2*F_16(x) + F_48(x) + F_57(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_54(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_54(x))
Eq(F_64(x), F_61(x))
Eq(F_65(x), F_118(x) + 2*F_16(x) + F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_72(x))
Eq(F_68(x), F_20(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_24(x))
Eq(F_72(x), F_107(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_80(x))
Eq(F_76(x), F_20(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_24(x))
Eq(F_80(x), F_73(x) + F_81(x))
Eq(F_81(x), 3*F_16(x) + F_82(x) + F_90(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_77(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_77(x))
Eq(F_89(x), F_86(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_97(x))
Eq(F_95(x), F_24(x) + F_96(x))
Eq(F_96(x), F_78(x))
Eq(F_97(x), F_92(x) + F_98(x))
Eq(F_98(x), 3*F_16(x) + F_90(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_96(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_106(x))
Eq(F_105(x), F_96(x))
Eq(F_106(x), F_103(x))
Eq(F_107(x), F_108(x) + F_116(x) + 3*F_16(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_69(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_69(x))
Eq(F_115(x), F_112(x))
Eq(F_116(x), F_117(x)*F_4(x))
Eq(F_117(x), F_92(x))
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x) + F_50(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_124(x) + F_126(x))
Eq(F_124(x), F_125(x) + F_24(x))
Eq(F_125(x), F_70(x))
Eq(F_126(x), F_127(x) + F_92(x))
Eq(F_127(x), F_116(x) + F_128(x) + 3*F_16(x))
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_130(x) + F_131(x))
Eq(F_130(x), F_125(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_133(x)*F_4(x))
Eq(F_133(x), F_134(x) + F_135(x))
Eq(F_134(x), F_125(x))
Eq(F_135(x), F_132(x))
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_138(x) + F_178(x))
Eq(F_138(x), F_139(x) + F_2(x))
Eq(F_139(x), F_140(x) + F_16(x) + F_177(x))
Eq(F_140(x), F_141(x)*F_4(x))
Eq(F_141(x), F_142(x) + F_146(x))
Eq(F_142(x), F_11(x) + F_143(x))
Eq(F_143(x), F_144(x) + F_16(x) + F_21(x))
Eq(F_144(x), F_145(x)*F_4(x))
Eq(F_145(x), F_143(x) + F_7(x))
Eq(F_146(x), F_147(x) + F_50(x))
Eq(F_147(x), F_118(x) + F_148(x) + 2*F_16(x))
Eq(F_148(x), F_149(x)*F_4(x))
Eq(F_149(x), F_150(x) + F_152(x))
Eq(F_150(x), F_143(x) + F_151(x))
Eq(F_151(x), F_70(x))
Eq(F_152(x), F_153(x) + F_168(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_155(x)*F_4(x))
Eq(F_155(x), F_156(x) + F_158(x))
Eq(F_156(x), F_143(x) + F_157(x))
Eq(F_157(x), F_78(x))
Eq(F_158(x), F_153(x) + F_159(x))
Eq(F_159(x), 3*F_16(x) + F_160(x) + F_90(x))
Eq(F_160(x), F_161(x)*F_4(x))
Eq(F_161(x), F_162(x) + F_163(x))
Eq(F_162(x), F_157(x))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_165(x)*F_4(x))
Eq(F_165(x), F_166(x) + F_167(x))
Eq(F_166(x), F_157(x))
Eq(F_167(x), F_164(x))
Eq(F_168(x), F_116(x) + 3*F_16(x) + F_169(x))
Eq(F_169(x), F_170(x)*F_4(x))
Eq(F_170(x), F_171(x) + F_172(x))
Eq(F_171(x), F_151(x))
Eq(F_172(x), F_173(x))
Eq(F_173(x), F_174(x)*F_4(x))
Eq(F_174(x), F_175(x) + F_176(x))
Eq(F_175(x), F_151(x))
Eq(F_176(x), F_173(x))
Eq(F_177(x), F_138(x)*F_4(x))
Eq(F_178(x), F_15(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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