0132_0321_1230_3012
Counting sequence:
1, 1, 2, 6, 20, 60, 161, 414, 1054, 2693, 6930, 17948, 46695, 121830, 318380, 832765, 2179216, 5704004, 14931709, 39089798, 102336090, 267916573, 701411390, 1836314980, 4807530515, 12586273070, 32951284696, 86267576469, 225851439564, 591286736428, 1548008763225, 4052739545998, 10610209866710, 27777890045205, 72723460259050, 190392490721100, 498454011892351, 1304969544942934, 3416454622922244, 8944394323808333, 23416728348485960, 61305790721631348, 160500643816388405, 420196140727512630, 1100087778366126610, 2880067194370842605, 7540113804746374806, 19740274219868253524, 51680708854858355499, 135301852344706780638, 354224848179261951920, 927372692193079038373, 2427893228399975124100, 6356306993006846292380, 16641027750620563708945, 43566776258854844787710, 114059301025943970604686, 298611126818977066973989, 781774079430987230261954, 2046711111473984623753468, 5358359254990966640936855, 14028366653498915298992198, 36726740705505779255971420, 96151855463018422468850205, 251728825683549488150503680, 659034621587630041982581540, 1725375039079340637797157741, 4517090495650391871408804454, 11825896447871834976429164234, 30960598847965113057878592573, 81055900096023504197206513390, 212207101440105399533740842948, 555565404224292694404015906115, 1454489111232772683678306761230, 3807901929474025356630904258440, 9969216677189303386214405889845, 26099748102093884802012313281596, 68330027629092351019822533820044, 178890334785183168257455288038089, 468340976726457153752543330148078, 1226132595394188293000174702254150, 3210056809456107725247980776456373, 8404037832974134882743767626950810, 22002056689466296922983322104225580, 57602132235424755886206198685548975, 150804340016807970735635273952237750, 394810887814999156320699623170973876, 1033628323428189498226463595560486509, 2706074082469569338358691163510281144, 7084593923980518516849609894970145108, 18547707689471986212190138521399934885, 48558529144435440119720805669229432598, 127127879743834334146972278486288128130, 332825110087067562321196029789634709005, 871347450517368352816615810882615747910, 2281217241465037496128651402858212275380, 5972304273877744135569338397692020810331, 15635695580168194910579363790217849878974, 40934782466626840596168752972961528541024, 107168651819712326877926895128666735449413, 280571172992510140037611932413038677503220
Generating function in Maple syntax:
(x^9-5*x^8+8*x^7-3*x^6-6*x^5+9*x^4-15*x^3+14*x^2-6*x+1)/(x^2-3*x+1)/(x-1)^4
Generating function in latex syntax:
\frac{x^{9}-5 x^{8}+8 x^{7}-3 x^{6}-6 x^{5}+9 x^{4}-15 x^{3}+14 x^{2}-6 x +1}{\left(x^{2}-3 x +1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(x**9 - 5*x**8 + 8*x**7 - 3*x**6 - 6*x**5 + 9*x**4 - 15*x**3 + 14*x**2 - 6*x + 1)/((x - 1)**4*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)*(x-1)^4*F(x)+x^9-5*x^8+8*x^7-3*x^6-6*x^5+9*x^4-15*x^3+14*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}-3 x +1\right) \left(x -1\right)^{4} F \! \left(x \right)+x^{9}-5 x^{8}+8 x^{7}-3 x^{6}-6 x^{5}+9 x^{4}-15 x^{3}+14 x^{2}-6 x +1 = 0
Explicit closed form in Maple syntax:
1/3*n^3-2*n^2+piecewise(n = 0,6,n = 1,3,n = 2,2,n = 3,1,0)+11/3*n-5-1/5*(3/2+1/2*5^(1/2))^(-n)*5^(1/2)+1/5*(3/2-1/2*5^(1/2))^(-n)*5^(1/2)
Explicit closed form in latex syntax:
\frac{n^{3}}{3}-2 n^{2}+\left(\left\{\begin{array}{cc}6 & n =0 \\ 3 & n =1 \\ 2 & n =2 \\ 1 & n =3 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{11 n}{3}-5-\frac{\left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{5}+\frac{\left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{5}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 60
a(6) = 161
a(7) = 414
a(8) = 1054
a(9) = 2693
a(n+2) = -1/3*n^3+n^2+3*a(n+1)-a(n)+4/3*n+1, n >= 10
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 60
a \! \left(6\right) = 161
a \! \left(7\right) = 414
a \! \left(8\right) = 1054
a \! \left(9\right) = 2693
a \! \left(n +2\right) = -\frac{n^{3}}{3}+n^{2}+3 a \! \left(n +1\right)-a \! \left(n \right)+\frac{4 n}{3}+1, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15448/
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[26,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[14,x]+F[17,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[1,x]+F[4,x]
F[17,x] = F[18,x]+F[19,x]+F[23,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[11,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]*F[4,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[14,x]+F[25,x]
F[25,x] = F[19,x]
F[26,x] = F[27,x]+F[65,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[1,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[16,x]*F[4,x]
F[33,x] = F[27,x]+F[34,x]
F[34,x] = F[18,x]+F[35,x]+F[63,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[41,x]
F[37,x] = F[31,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[4,x]
F[41,x] = F[34,x]+F[42,x]
F[42,x] = 2*F[18,x]+F[43,x]+F[47,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[38,x]
F[46,x] = F[42,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[18,x]+F[50,x]+F[62,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[55,x]
F[52,x] = F[4,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = x^2
F[55,x] = F[49,x]+F[56,x]
F[56,x] = 2*F[18,x]+F[57,x]+F[61,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[53,x]
F[60,x] = F[56,x]
F[61,x] = F[4,x]*F[49,x]
F[62,x] = F[27,x]*F[4,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[27,x]+F[49,x]
F[65,x] = F[168,x]+F[18,x]+F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[82,x]
F[68,x] = F[69,x]+F[7,x]
F[69,x] = F[18,x]+F[70,x]+F[75,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[11,x]+F[72,x]
F[72,x] = F[18,x]+F[22,x]+F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[21,x]+F[4,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[74,x]+F[77,x]
F[77,x] = F[78,x]+F[80,x]
F[78,x] = F[79,x]
F[79,x] = x^2
F[80,x] = F[81,x]
F[81,x] = F[21,x]*F[4,x]
F[82,x] = F[65,x]+F[83,x]
F[83,x] = F[137,x]+F[150,x]+F[18,x]+F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]+F[90,x]
F[86,x] = F[69,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[21,x]
F[90,x] = F[83,x]+F[91,x]
F[91,x] = 2*F[18,x]+F[136,x]+F[92,x]+F[96,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[87,x]
F[95,x] = F[91,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = 2*F[18,x]+F[111,x]+F[99,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[101,x]+F[104,x]
F[101,x] = F[102,x]+F[21,x]
F[102,x] = F[103,x]
F[103,x] = F[21,x]*F[4,x]
F[104,x] = F[105,x]+F[98,x]
F[105,x] = 3*F[18,x]+F[106,x]+F[110,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[102,x]
F[109,x] = F[105,x]
F[110,x] = F[4,x]*F[98,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[115,x]+F[118,x]
F[115,x] = F[11,x]+F[116,x]
F[116,x] = F[117,x]
F[117,x] = F[20,x]*F[4,x]
F[118,x] = F[112,x]+F[119,x]
F[119,x] = 2*F[18,x]+F[120,x]+F[134,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[126,x]
F[122,x] = F[116,x]+F[123,x]
F[123,x] = F[124,x]
F[124,x] = F[125,x]*F[4,x]
F[125,x] = F[21,x]
F[126,x] = F[119,x]+F[127,x]
F[127,x] = 3*F[18,x]+F[128,x]+F[132,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[130,x]+F[131,x]
F[130,x] = F[123,x]
F[131,x] = F[127,x]
F[132,x] = F[133,x]*F[4,x]
F[133,x] = F[98,x]
F[134,x] = F[135,x]*F[4,x]
F[135,x] = F[112,x]+F[98,x]
F[136,x] = 0
F[137,x] = F[138,x]*F[4,x]
F[138,x] = F[112,x]+F[139,x]
F[139,x] = 2*F[18,x]+F[111,x]+F[140,x]
F[140,x] = F[141,x]*F[4,x]
F[141,x] = F[142,x]+F[144,x]
F[142,x] = F[143,x]+F[72,x]
F[143,x] = F[103,x]
F[144,x] = F[139,x]+F[145,x]
F[145,x] = 3*F[18,x]+F[110,x]+F[146,x]
F[146,x] = F[147,x]*F[4,x]
F[147,x] = F[148,x]+F[149,x]
F[148,x] = F[143,x]
F[149,x] = F[145,x]
F[150,x] = F[151,x]*F[4,x]
F[151,x] = F[152,x]+F[153,x]
F[152,x] = F[49,x]+F[98,x]
F[153,x] = F[154,x]+F[161,x]
F[154,x] = F[155,x]
F[155,x] = F[156,x]*F[4,x]
F[156,x] = F[157,x]
F[157,x] = F[158,x]*F[4,x]
F[158,x] = F[159,x]+F[160,x]
F[159,x] = F[4,x]
F[160,x] = F[156,x]
F[161,x] = F[162,x]
F[162,x] = F[163,x]*F[4,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[21,x]
F[167,x] = F[163,x]
F[168,x] = F[169,x]*F[4,x]
F[169,x] = F[170,x]+F[171,x]
F[170,x] = F[112,x]+F[27,x]
F[171,x] = F[172,x]+F[175,x]
F[172,x] = F[173,x]+F[18,x]+F[50,x]
F[173,x] = F[174,x]*F[4,x]
F[174,x] = F[156,x]+F[27,x]
F[175,x] = 2*F[18,x]+F[140,x]+F[176,x]
F[176,x] = F[177,x]*F[4,x]
F[177,x] = F[112,x]+F[163,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_{26}\! \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_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{11}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{19}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{65}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
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_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{27}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{18}\! \left(x \right)+F_{35}\! \left(x \right)+F_{63}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{37}\! \left(x \right) = F_{31}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{43}\! \left(x \right)+F_{47}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{38}\! \left(x \right)
F_{46}\! \left(x \right) = F_{42}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{18}\! \left(x \right)+F_{50}\! \left(x \right)+F_{62}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{55}\! \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_{54}\! \left(x \right) = x^{2}
F_{55}\! \left(x \right) = F_{49}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{57}\! \left(x \right)+F_{61}\! \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_{53}\! \left(x \right)
F_{60}\! \left(x \right) = F_{56}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{62}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{27}\! \left(x \right)+F_{49}\! \left(x \right)
F_{65}\! \left(x \right) = F_{168}\! \left(x \right)+F_{18}\! \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_{82}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{7}\! \left(x \right)
F_{69}\! \left(x \right) = F_{18}\! \left(x \right)+F_{70}\! \left(x \right)+F_{75}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{11}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{21}\! \left(x \right)+F_{4}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{74}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{80}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = x^{2}
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{82}\! \left(x \right) = F_{65}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{137}\! \left(x \right)+F_{150}\! \left(x \right)+F_{18}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{90}\! \left(x \right)
F_{86}\! \left(x \right) = F_{69}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{21}\! \left(x \right)
F_{90}\! \left(x \right) = F_{83}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{136}\! \left(x \right)+F_{92}\! \left(x \right)+F_{96}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{87}\! \left(x \right)
F_{95}\! \left(x \right) = F_{91}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{111}\! \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_{104}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{21}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{98}\! \left(x \right)
F_{105}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{106}\! \left(x \right)+F_{110}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{102}\! \left(x \right)
F_{109}\! \left(x \right) = F_{105}\! \left(x \right)
F_{110}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{118}\! \left(x \right)
F_{115}\! \left(x \right) = F_{11}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{112}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{120}\! \left(x \right)+F_{134}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{126}\! \left(x \right)
F_{122}\! \left(x \right) = F_{116}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{4}\! \left(x \right)
F_{125}\! \left(x \right) = F_{21}\! \left(x \right)
F_{126}\! \left(x \right) = F_{119}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{128}\! \left(x \right)+F_{132}\! \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_{123}\! \left(x \right)
F_{131}\! \left(x \right) = F_{127}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{98}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{4}\! \left(x \right)
F_{135}\! \left(x \right) = F_{112}\! \left(x \right)+F_{98}\! \left(x \right)
F_{136}\! \left(x \right) = 0
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{4}\! \left(x \right)
F_{138}\! \left(x \right) = F_{112}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{111}\! \left(x \right)+F_{140}\! \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_{144}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{72}\! \left(x \right)
F_{143}\! \left(x \right) = F_{103}\! \left(x \right)
F_{144}\! \left(x \right) = F_{139}\! \left(x \right)+F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{110}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right) F_{4}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{149}\! \left(x \right)
F_{148}\! \left(x \right) = F_{143}\! \left(x \right)
F_{149}\! \left(x \right) = F_{145}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right) F_{4}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{153}\! \left(x \right)
F_{152}\! \left(x \right) = F_{49}\! \left(x \right)+F_{98}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{161}\! \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_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{4}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{160}\! \left(x \right)
F_{159}\! \left(x \right) = F_{4}\! \left(x \right)
F_{160}\! \left(x \right) = F_{156}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right) F_{4}\! \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_{21}\! \left(x \right)
F_{167}\! \left(x \right) = F_{163}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right) F_{4}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{171}\! \left(x \right)
F_{170}\! \left(x \right) = F_{112}\! \left(x \right)+F_{27}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{175}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{18}\! \left(x \right)+F_{50}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right) F_{4}\! \left(x \right)
F_{174}\! \left(x \right) = F_{156}\! \left(x \right)+F_{27}\! \left(x \right)
F_{175}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{140}\! \left(x \right)+F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right) F_{4}\! \left(x \right)
F_{177}\! \left(x \right) = F_{112}\! \left(x \right)+F_{163}\! \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_26(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_14(x) + F_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_1(x) + F_4(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_23(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_11(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)*F_4(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_14(x) + F_25(x))
Eq(F_25(x), F_19(x))
Eq(F_26(x), F_27(x) + F_65(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_1(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_16(x)*F_4(x))
Eq(F_33(x), F_27(x) + F_34(x))
Eq(F_34(x), F_18(x) + F_35(x) + F_63(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_41(x))
Eq(F_37(x), F_31(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_4(x))
Eq(F_41(x), F_34(x) + F_42(x))
Eq(F_42(x), 2*F_18(x) + F_43(x) + F_47(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_38(x))
Eq(F_46(x), F_42(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_18(x) + F_50(x) + F_62(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_55(x))
Eq(F_52(x), F_4(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), x**2)
Eq(F_55(x), F_49(x) + F_56(x))
Eq(F_56(x), 2*F_18(x) + F_57(x) + F_61(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_53(x))
Eq(F_60(x), F_56(x))
Eq(F_61(x), F_4(x)*F_49(x))
Eq(F_62(x), F_27(x)*F_4(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_27(x) + F_49(x))
Eq(F_65(x), F_168(x) + F_18(x) + F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_82(x))
Eq(F_68(x), F_69(x) + F_7(x))
Eq(F_69(x), F_18(x) + F_70(x) + F_75(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_11(x) + F_72(x))
Eq(F_72(x), F_18(x) + F_22(x) + F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_21(x) + F_4(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_74(x) + F_77(x))
Eq(F_77(x), F_78(x) + F_80(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), x**2)
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_21(x)*F_4(x))
Eq(F_82(x), F_65(x) + F_83(x))
Eq(F_83(x), F_137(x) + F_150(x) + F_18(x) + F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_90(x))
Eq(F_86(x), F_69(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_21(x))
Eq(F_90(x), F_83(x) + F_91(x))
Eq(F_91(x), F_136(x) + 2*F_18(x) + F_92(x) + F_96(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_87(x))
Eq(F_95(x), F_91(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_111(x) + 2*F_18(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_101(x) + F_104(x))
Eq(F_101(x), F_102(x) + F_21(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_21(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_98(x))
Eq(F_105(x), F_106(x) + F_110(x) + 3*F_18(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_102(x))
Eq(F_109(x), F_105(x))
Eq(F_110(x), F_4(x)*F_98(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_115(x) + F_118(x))
Eq(F_115(x), F_11(x) + F_116(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_20(x)*F_4(x))
Eq(F_118(x), F_112(x) + F_119(x))
Eq(F_119(x), F_120(x) + F_134(x) + 2*F_18(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_126(x))
Eq(F_122(x), F_116(x) + F_123(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_125(x)*F_4(x))
Eq(F_125(x), F_21(x))
Eq(F_126(x), F_119(x) + F_127(x))
Eq(F_127(x), F_128(x) + F_132(x) + 3*F_18(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_123(x))
Eq(F_131(x), F_127(x))
Eq(F_132(x), F_133(x)*F_4(x))
Eq(F_133(x), F_98(x))
Eq(F_134(x), F_135(x)*F_4(x))
Eq(F_135(x), F_112(x) + F_98(x))
Eq(F_136(x), 0)
Eq(F_137(x), F_138(x)*F_4(x))
Eq(F_138(x), F_112(x) + F_139(x))
Eq(F_139(x), F_111(x) + F_140(x) + 2*F_18(x))
Eq(F_140(x), F_141(x)*F_4(x))
Eq(F_141(x), F_142(x) + F_144(x))
Eq(F_142(x), F_143(x) + F_72(x))
Eq(F_143(x), F_103(x))
Eq(F_144(x), F_139(x) + F_145(x))
Eq(F_145(x), F_110(x) + F_146(x) + 3*F_18(x))
Eq(F_146(x), F_147(x)*F_4(x))
Eq(F_147(x), F_148(x) + F_149(x))
Eq(F_148(x), F_143(x))
Eq(F_149(x), F_145(x))
Eq(F_150(x), F_151(x)*F_4(x))
Eq(F_151(x), F_152(x) + F_153(x))
Eq(F_152(x), F_49(x) + F_98(x))
Eq(F_153(x), F_154(x) + F_161(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))
Eq(F_157(x), F_158(x)*F_4(x))
Eq(F_158(x), F_159(x) + F_160(x))
Eq(F_159(x), F_4(x))
Eq(F_160(x), F_156(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_163(x)*F_4(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_21(x))
Eq(F_167(x), F_163(x))
Eq(F_168(x), F_169(x)*F_4(x))
Eq(F_169(x), F_170(x) + F_171(x))
Eq(F_170(x), F_112(x) + F_27(x))
Eq(F_171(x), F_172(x) + F_175(x))
Eq(F_172(x), F_173(x) + F_18(x) + F_50(x))
Eq(F_173(x), F_174(x)*F_4(x))
Eq(F_174(x), F_156(x) + F_27(x))
Eq(F_175(x), F_140(x) + F_176(x) + 2*F_18(x))
Eq(F_176(x), F_177(x)*F_4(x))
Eq(F_177(x), F_112(x) + F_163(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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