0123_0213_0231_1302_2130
Counting sequence:
1, 1, 2, 6, 19, 55, 148, 378, 933, 2254, 5373, 12700, 29855, 69931, 163411, 381233, 888427, 2068834, 4815088, 11202816, 26058082, 60601445, 140919678, 327660630, 761819042, 1771176977, 4117749937, 9573032754, 22255289640, 51738385437, 120278956104, 279617565439, 650036694178, 1511159610703, 3513032236715, 8166829113329, 18985606635139, 44136233003707, 102604378100224, 238526377262620, 554506774171330, 1289072214003342, 2996729904424497, 6966552760846946, 16195271822598434, 37649441686837890, 87524337147378903, 203469404698586423, 473008989266581488, 1099612508136219634, 2556288970939093513, 5942650918762702950, 13814987375862432725, 32115949347268557156, 74660524348427371511, 173564661952458866763, 403488886873225710687, 937997861654473500029, 2180580474126149971623, 5069234587490737381526, 11784540678379116483432, 27395733338334764196860, 63687353252294267325198, 148055133769202599923145, 344186428158521709493582, 800136370217232085995062, 1860091388148801009134142, 4324187852243184025154149, 10052517150766851173650345, 23369267136153378970486142, 54326954959477680110482144, 126294847757391587576003889, 293599900490179297010583048, 682536960916537365535152303, 1586705929528756575238272890, 3688643767246790746278003959, 8575056403604924393593503299, 19934587605858892657786566477, 46342293777628092266475373159, 107732762524794832605794957655, 250448287625025095004593837180, 582221631603175017859388581132, 1353501082084368891027867782342, 3146508270671942233013236389186, 7314744279450523630340273306749, 17004717379092475512162942414050, 39531171849049001400459155630258, 91898825068413676895170221471518, 213638848886237283376171300282443, 496650068370936377805826984350839, 1154571332408752903606918949489628, 2684052709370630778699078926396250, 6239665531665335106849640986437245, 14505462508663516407031903924232206, 33721109172030541726530143716318461, 78392068030429979153085119145251468, 182239448255892454034370463775772847, 423655317878848080825323641459880299, 984879125155189532483310950528515883, 2289566187963765244058504211703475161, 5322595631459765321182058389330358307
Generating function in Maple syntax:
-(x^8+x^7+x^6-x^5+5*x^3-9*x^2+5*x-1)/(x^2+x-1)/(x^3-2*x^2+3*x-1)/(-1+x)^2
Generating function in latex syntax:
-\frac{x^{8}+x^{7}+x^{6}-x^{5}+5 x^{3}-9 x^{2}+5 x -1}{\left(x^{2}+x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(-1+x \right)^{2}}
Generating function in sympy syntax:
(-x**8 - x**7 - x**6 + x**5 - 5*x**3 + 9*x**2 - 5*x + 1)/((x - 1)**2*(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)*(-1+x)^2*F(x)+x^8+x^7+x^6-x^5+5*x^3-9*x^2+5*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(-1+x \right)^{2} F \! \left(x \right)+x^{8}+x^{7}+x^{6}-x^{5}+5 x^{3}-9 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/69000*(-2208*2^(1/3)*((I-167/1104*23^(1/2))*3^(1/2)-167/368*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(2/3)+27600+4485*((I-59/897*23^(1/2))*3^(1/2)+59/299*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)+1/69000*(-4485*((I+59/897*23^(1/2))*3^(1/2)+59/299*I*23^(1/2)+1)*2^(2/3)*(11+3*23^(1/2)*3^(1/2))^(1/3)+27600+2208*2^(1/3)*((I+167/1104*23^(1/2))*3^(1/2)-167/368*I*23^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(2/3))*(-11/600*((I+3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)-1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+1/12*I*3^(1/2)*(44+12*23^(1/2)*3^(1/2))^(1/3)+1/12*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/69000*((590*3^(1/2)*2^(2/3)*23^(1/2)+8970*2^(2/3))*(11+3*23^(1/2)*3^(1/2))^(1/3)+27600+(-668*23^(1/2)*3^(1/2)*2^(1/3)+4416*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)+1/69000*(34500*5^(1/2)-75900)*(-1/2*5^(1/2)-1/2)^(-n)+1/69000*(-34500*5^(1/2)-75900)*(1/2*5^(1/2)-1/2)^(-n)-2*n+6)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(-2208 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{167 \sqrt{23}}{1104}\right) \sqrt{3}-\frac{167 \,\mathrm{I} \sqrt{23}}{368}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+27600+4485 \left(\left(\mathrm{I}-\frac{59 \sqrt{23}}{897}\right) \sqrt{3}+\frac{59 \,\mathrm{I} \sqrt{23}}{299}-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}}{69000}\\+\\\frac{\left(-4485 \left(\left(\mathrm{I}+\frac{59 \sqrt{23}}{897}\right) \sqrt{3}+\frac{59 \,\mathrm{I} \sqrt{23}}{299}+1\right) 2^{\frac{2}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+27600+2208 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{167 \sqrt{23}}{1104}\right) \sqrt{3}-\frac{167 \,\mathrm{I} \sqrt{23}}{368}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{11 \left(\left(\mathrm{I}+\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}-1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{600}+\frac{\mathrm{I} \sqrt{3}\, \left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{69000}\\+\\\frac{\left(\left(590 \sqrt{3}\, 2^{\frac{2}{3}} \sqrt{23}+8970 \,2^{\frac{2}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+27600+\left(-668 \sqrt{23}\, \sqrt{3}\, 2^{\frac{1}{3}}+4416 \,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}}{69000}\\+\frac{\left(34500 \sqrt{5}-75900\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{69000}+\\\frac{\left(-34500 \sqrt{5}-75900\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{69000}-2 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) = 55
a(6) = 148
a(7) = 378
a(8) = 933
a(n+1) = a(n)+4*a(n+3)-4*a(n+4)+a(n+5)+2*n-6, 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) = 19
a \! \left(5\right) = 55
a \! \left(6\right) = 148
a \! \left(7\right) = 378
a \! \left(8\right) = 933
a \! \left(n +1\right) = a \! \left(n \right)+4 a \! \left(n +3\right)-4 a \! \left(n +4\right)+a \! \left(n +5\right)+2 n -6, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16741/
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[27,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[181,x]
F[138,x] = F[139,x]+F[2,x]
F[139,x] = F[140,x]+F[16,x]+F[178,x]
F[140,x] = F[141,x]*F[4,x]
F[141,x] = F[142,x]+F[147,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[146,x]+F[7,x]
F[146,x] = F[144,x]
F[147,x] = F[148,x]+F[50,x]
F[148,x] = 2*F[16,x]+F[118,x]+F[149,x]
F[149,x] = F[150,x]*F[4,x]
F[150,x] = F[151,x]+F[153,x]
F[151,x] = F[143,x]+F[152,x]
F[152,x] = F[70,x]
F[153,x] = F[154,x]+F[169,x]
F[154,x] = F[155,x]
F[155,x] = F[156,x]*F[4,x]
F[156,x] = F[157,x]+F[159,x]
F[157,x] = F[143,x]+F[158,x]
F[158,x] = F[78,x]
F[159,x] = F[154,x]+F[160,x]
F[160,x] = 3*F[16,x]+F[161,x]+F[90,x]
F[161,x] = F[162,x]*F[4,x]
F[162,x] = F[163,x]+F[164,x]
F[163,x] = F[158,x]
F[164,x] = F[165,x]
F[165,x] = F[166,x]*F[4,x]
F[166,x] = F[167,x]+F[168,x]
F[167,x] = F[158,x]
F[168,x] = F[165,x]
F[169,x] = 3*F[16,x]+F[116,x]+F[170,x]
F[170,x] = F[171,x]*F[4,x]
F[171,x] = F[172,x]+F[173,x]
F[172,x] = F[152,x]
F[173,x] = F[174,x]
F[174,x] = F[175,x]*F[4,x]
F[175,x] = F[176,x]+F[177,x]
F[176,x] = F[152,x]
F[177,x] = F[174,x]
F[178,x] = F[179,x]*F[4,x]
F[179,x] = F[180,x]+F[2,x]
F[180,x] = F[178,x]
F[181,x] = F[182,x]
F[182,x] = F[183,x]*F[4,x]
F[183,x] = F[179,x]+F[184,x]
F[184,x] = F[182,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_{27}\! \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_{181}\! \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_{178}\! \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_{147}\! \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_{146}\! \left(x \right)+F_{7}\! \left(x \right)
F_{146}\! \left(x \right) = F_{144}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{50}\! \left(x \right)
F_{148}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{118}\! \left(x \right)+F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{4}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{153}\! \left(x \right)
F_{151}\! \left(x \right) = F_{143}\! \left(x \right)+F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{70}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{169}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right) F_{4}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{159}\! \left(x \right)
F_{157}\! \left(x \right) = F_{143}\! \left(x \right)+F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{78}\! \left(x \right)
F_{159}\! \left(x \right) = F_{154}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{161}\! \left(x \right)+F_{90}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right) F_{4}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{164}\! \left(x \right)
F_{163}\! \left(x \right) = F_{158}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{4}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{168}\! \left(x \right)
F_{167}\! \left(x \right) = F_{158}\! \left(x \right)
F_{168}\! \left(x \right) = F_{165}\! \left(x \right)
F_{169}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{116}\! \left(x \right)+F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{4}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{173}\! \left(x \right)
F_{172}\! \left(x \right) = F_{152}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right) F_{4}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)+F_{177}\! \left(x \right)
F_{176}\! \left(x \right) = F_{152}\! \left(x \right)
F_{177}\! \left(x \right) = F_{174}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right) F_{4}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{2}\! \left(x \right)
F_{180}\! \left(x \right) = F_{178}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right) F_{4}\! \left(x \right)
F_{183}\! \left(x \right) = F_{179}\! \left(x \right)+F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{182}\! \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_27(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_181(x))
Eq(F_138(x), F_139(x) + F_2(x))
Eq(F_139(x), F_140(x) + F_16(x) + F_178(x))
Eq(F_140(x), F_141(x)*F_4(x))
Eq(F_141(x), F_142(x) + F_147(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_146(x) + F_7(x))
Eq(F_146(x), F_144(x))
Eq(F_147(x), F_148(x) + F_50(x))
Eq(F_148(x), F_118(x) + F_149(x) + 2*F_16(x))
Eq(F_149(x), F_150(x)*F_4(x))
Eq(F_150(x), F_151(x) + F_153(x))
Eq(F_151(x), F_143(x) + F_152(x))
Eq(F_152(x), F_70(x))
Eq(F_153(x), F_154(x) + F_169(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_156(x)*F_4(x))
Eq(F_156(x), F_157(x) + F_159(x))
Eq(F_157(x), F_143(x) + F_158(x))
Eq(F_158(x), F_78(x))
Eq(F_159(x), F_154(x) + F_160(x))
Eq(F_160(x), 3*F_16(x) + F_161(x) + F_90(x))
Eq(F_161(x), F_162(x)*F_4(x))
Eq(F_162(x), F_163(x) + F_164(x))
Eq(F_163(x), F_158(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_166(x)*F_4(x))
Eq(F_166(x), F_167(x) + F_168(x))
Eq(F_167(x), F_158(x))
Eq(F_168(x), F_165(x))
Eq(F_169(x), F_116(x) + 3*F_16(x) + F_170(x))
Eq(F_170(x), F_171(x)*F_4(x))
Eq(F_171(x), F_172(x) + F_173(x))
Eq(F_172(x), F_152(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_175(x)*F_4(x))
Eq(F_175(x), F_176(x) + F_177(x))
Eq(F_176(x), F_152(x))
Eq(F_177(x), F_174(x))
Eq(F_178(x), F_179(x)*F_4(x))
Eq(F_179(x), F_180(x) + F_2(x))
Eq(F_180(x), F_178(x))
Eq(F_181(x), F_182(x))
Eq(F_182(x), F_183(x)*F_4(x))
Eq(F_183(x), F_179(x) + F_184(x))
Eq(F_184(x), F_182(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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