0123_0132_0213_1320_3021

Counting sequence:
1, 1, 2, 6, 19, 56, 150, 379, 933, 2279, 5583, 13791, 34408, 86668, 220085, 562562, 1445389, 3728512, 9647988, 25026127, 65040059, 169287487, 441153761, 1150720083, 3003858438, 7846066756, 20503764135, 53602045614, 140171929483, 366644639944, 959207276478, 2509834631291, 6567945064313, 17189164308863, 44989608634795, 117759249019247, 308246243950684, 806893553528612, 2112258274550353, 5529520414569602, 14475564108153089, 37895659876578552, 99208322813797056, 259722985836933263, 679947714568175983, 1780093768185477031, 4660279711648430445, 12200635411924130099, 31941402217809153258, 83623113835050781484, 218927006885924982323, 573156006841458426366, 1500537143316790063343, 3928447541743660827408, 10284789437733886811130, 26925888120188165466507, 70492808494456937542429, 184552402254742122524087, 483164123549461289131943, 1264939409946105376711327, 3311652971379835298768944, 8670017198347295287513692, 22698393939913428635953101, 59425155109782472133776418, 155577052077985670658973653, 407305961924822162789482256, 1066340754144862664475449580, 2791716139100699629896910959, 7308807335727439025728922883, 19134705203998685346824020399, 50095306929656064295883371993, 131151212854851003846829363891, 343358326100873109008695117998, 898923754232146929455822965428, 2353412913869177367517538093215, 6161314941332309355178658511342, 16130531816861008438372786280499, 42230280320356049812244643608312, 110560308761695444830040477972758, 289450645190262163598466325050427, 757791625241265344707968234105249, 1983924227360103547203580093803407, 5193981050416626804421929807312771, 13598018910893824182593364253581423, 35600075655970708968350272210654948, 93202208003825566338412481054997556, 244006548247911591581794180579482665, 638817436522302560035944527777412194, 1672445760878947088826531107878340233, 4378519845224769301007106166537317064, 11463113772996479191048260347756842488, 30010821470128219400976735930470634991, 78569350630037910019304908840685462903, 205697230405130230170433199683298350423, 538522340555332734514923897712656613925, 1409869791200208911409874311544872252627, 3691087032922737935761565520436960685394, 9663391307320416887914384777076462088412, 25299086888538384951943052892753476050923, 66233869357284578895587299892176860427902, 173402521181275226549638694099074231105879

Generating function in Maple syntax:
(4*x^15-20*x^14+20*x^13+36*x^12-73*x^11+12*x^10+95*x^9-136*x^8+54*x^7+134*x^6-301*x^5+304*x^4-178*x^3+62*x^2-12*x+1)/(x^2-3*x+1)/(x^2+x-1)/(2*x-1)^2/(x-1)^5

Generating function in latex syntax:
\frac{4 x^{15}-20 x^{14}+20 x^{13}+36 x^{12}-73 x^{11}+12 x^{10}+95 x^{9}-136 x^{8}+54 x^{7}+134 x^{6}-301 x^{5}+304 x^{4}-178 x^{3}+62 x^{2}-12 x +1}{\left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{5}}

Generating function in sympy syntax:
(4*x**15 - 20*x**14 + 20*x**13 + 36*x**12 - 73*x**11 + 12*x**10 + 95*x**9 - 136*x**8 + 54*x**7 + 134*x**6 - 301*x**5 + 304*x**4 - 178*x**3 + 62*x**2 - 12*x + 1)/((x - 1)**5*(2*x - 1)**2*(x**2 - 3*x + 1)*(x**2 + x - 1))

Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)*(x^2+x-1)*(2*x-1)^2*(x-1)^5*F(x)+4*x^15-20*x^14+20*x^13+36*x^12-73*x^11+12*x^10+95*x^9-136*x^8+54*x^7+134*x^6-301*x^5+304*x^4-178*x^3+62*x^2-12*x+1 = 0

Implicit equation for the generating function in latex syntax:
-\left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{5} F \! \left(x \right)+4 x^{15}-20 x^{14}+20 x^{13}+36 x^{12}-73 x^{11}+12 x^{10}+95 x^{9}-136 x^{8}+54 x^{7}+134 x^{6}-301 x^{5}+304 x^{4}-178 x^{3}+62 x^{2}-12 x +1 = 0

Explicit closed form in Maple syntax:
1/12*n^4-n^3+1/16*2^n*n+53/12*n^2+7/16*2^n+piecewise(n = 0,-23/16,n = 1,4,n = 2,19/4,n = 3,3,n = 4,1,0)-21/2*n+3/10*(1/2*5^(1/2)-1/2)^(-n)*5^(1/2)-1/10*(3/2-1/2*5^(1/2))^(-n)*5^(1/2)-3/10*(-1/2*5^(1/2)-1/2)^(-n)*5^(1/2)+1/10*(3/2+1/2*5^(1/2))^(-n)*5^(1/2)+1/2*(1/2*5^(1/2)-1/2)^(-n)+1/2*(3/2-1/2*5^(1/2))^(-n)+1/2*(-1/2*5^(1/2)-1/2)^(-n)+1/2*(3/2+1/2*5^(1/2))^(-n)

Explicit closed form in latex syntax:
\frac{n^{4}}{12}-n^{3}+\frac{2^{n} n}{16}+\frac{53 n^{2}}{12}+\frac{7 \,2^{n}}{16}+\left(\left\{\begin{array}{cc}-\frac{23}{16} & n =0 \\ 4 & n =1 \\ \frac{19}{4} & n =2 \\ 3 & n =3 \\ 1 & n =4 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)-\frac{21 n}{2}+\frac{3 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n} \sqrt{5}}{10}-\frac{\left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{10}-\frac{3 \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n} \sqrt{5}}{10}+\frac{\left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{10}+\frac{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{2}+\frac{\left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{2}+\frac{\left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{2}+\frac{\left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{2}

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 56
a(6) = 150
a(7) = 379
a(8) = 933
a(9) = 2279
a(10) = 5583
a(11) = 13791
a(12) = 34408
a(13) = 86668
a(14) = 220085
a(15) = 562562
a(n+6) = 1/12*n^4-5/3*n^3+89/12*n^2-12*a(n+1)-3*a(n+2)+26*a(n+3)-23*a(n+4)+8*a(n+5)+4*a(n)-17/6*n-16, n >= 16

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) = 56
a \! \left(6\right) = 150
a \! \left(7\right) = 379
a \! \left(8\right) = 933
a \! \left(9\right) = 2279
a \! \left(10\right) = 5583
a \! \left(11\right) = 13791
a \! \left(12\right) = 34408
a \! \left(13\right) = 86668
a \! \left(14\right) = 220085
a \! \left(15\right) = 562562
a \! \left(n +6\right) = \frac{n^{4}}{12}-\frac{5 n^{3}}{3}+\frac{89 n^{2}}{12}-12 a \! \left(n +1\right)-3 a \! \left(n +2\right)+26 a \! \left(n +3\right)-23 a \! \left(n +4\right)+8 a \! \left(n +5\right)+4 a \! \left(n \right)-\frac{17 n}{6}-16, \quad n \geq 16

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16023/
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[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[7,x]
F[12,x] = F[13,x]
F[13,x] = F[4,x]*F[7,x]
F[14,x] = F[15,x]+F[52,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[1,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[10,x]*F[4,x]
F[21,x] = F[15,x]+F[22,x]
F[22,x] = F[23,x]+F[24,x]+F[50,x]
F[23,x] = 0
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[30,x]
F[26,x] = F[19,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[4,x]
F[30,x] = F[22,x]+F[31,x]
F[31,x] = 2*F[23,x]+F[32,x]+F[36,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[27,x]
F[35,x] = F[31,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]
F[38,x] = F[23,x]+F[39,x]+F[49,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]+F[43,x]
F[41,x] = F[4,x]+F[42,x]
F[42,x] = F[28,x]
F[43,x] = F[38,x]+F[44,x]
F[44,x] = 2*F[23,x]+F[36,x]+F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[42,x]
F[48,x] = F[44,x]
F[49,x] = F[15,x]*F[4,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[15,x]+F[38,x]
F[52,x] = F[154,x]+F[23,x]+F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[66,x]
F[55,x] = F[56,x]+F[7,x]
F[56,x] = F[23,x]+F[28,x]+F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[62,x]
F[59,x] = F[19,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[19,x]*F[4,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[28,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[63,x]
F[66,x] = F[52,x]+F[67,x]
F[67,x] = F[135,x]+F[23,x]+F[68,x]+F[97,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[77,x]
F[70,x] = F[56,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[27,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[27,x]*F[4,x]
F[77,x] = F[67,x]+F[78,x]
F[78,x] = 2*F[23,x]+F[79,x]+F[83,x]+F[84,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[71,x]
F[82,x] = F[78,x]
F[83,x] = 0
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]
F[86,x] = F[87,x]+F[91,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[34,x]+F[90,x]
F[90,x] = F[87,x]
F[91,x] = 3*F[23,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[75,x]
F[95,x] = F[91,x]
F[96,x] = F[4,x]*F[87,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]+F[23,x]+F[49,x]
F[100,x] = F[101,x]*F[4,x]
F[101,x] = F[102,x]+F[104,x]
F[102,x] = F[103,x]+F[4,x]
F[103,x] = F[23,x]+F[28,x]+F[61,x]
F[104,x] = F[105,x]+F[99,x]
F[105,x] = F[106,x]+F[116,x]+F[23,x]+F[97,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[108,x]+F[110,x]
F[108,x] = F[103,x]+F[109,x]
F[109,x] = F[76,x]
F[110,x] = F[105,x]+F[111,x]
F[111,x] = 2*F[23,x]+F[112,x]+F[83,x]+F[96,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[109,x]
F[115,x] = F[111,x]
F[116,x] = F[117,x]*F[4,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[120,x]+F[26,x]
F[120,x] = F[117,x]+F[121,x]
F[121,x] = 2*F[23,x]+F[122,x]+F[125,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[124,x]+F[34,x]
F[124,x] = F[121,x]
F[125,x] = F[126,x]*F[4,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[130,x]+F[41,x]
F[130,x] = F[127,x]+F[131,x]
F[131,x] = 2*F[23,x]+F[125,x]+F[132,x]
F[132,x] = F[133,x]*F[4,x]
F[133,x] = F[134,x]+F[47,x]
F[134,x] = F[131,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[137,x]+F[150,x]
F[137,x] = F[117,x]+F[138,x]
F[138,x] = 2*F[23,x]+F[116,x]+F[139,x]
F[139,x] = F[140,x]*F[4,x]
F[140,x] = F[141,x]+F[143,x]
F[141,x] = F[142,x]+F[60,x]
F[142,x] = F[76,x]
F[143,x] = F[138,x]+F[144,x]
F[144,x] = 2*F[23,x]+F[145,x]+F[149,x]+F[96,x]
F[145,x] = F[146,x]*F[4,x]
F[146,x] = F[147,x]+F[148,x]
F[147,x] = F[142,x]
F[148,x] = F[144,x]
F[149,x] = 0
F[150,x] = F[151,x]+F[152,x]
F[151,x] = F[88,x]
F[152,x] = 3*F[23,x]+F[153,x]+F[92,x]
F[153,x] = F[151,x]*F[4,x]
F[154,x] = F[155,x]*F[4,x]
F[155,x] = F[156,x]+F[157,x]
F[156,x] = F[15,x]+F[99,x]
F[157,x] = F[158,x]+F[159,x]
F[158,x] = F[118,x]
F[159,x] = 2*F[23,x]+F[139,x]+F[160,x]
F[160,x] = F[158,x]*F[4,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_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{52}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \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_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{50}\! \left(x \right)
F_{23}\! \left(x \right) = 0
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{26}\! \left(x \right) = F_{19}\! \left(x \right)+F_{27}\! \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_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{22}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{32}\! \left(x \right)+F_{36}\! \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_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{27}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{23}\! \left(x \right)+F_{39}\! \left(x \right)+F_{49}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{28}\! \left(x \right)
F_{43}\! \left(x \right) = F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{36}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{42}\! \left(x \right)
F_{48}\! \left(x \right) = F_{44}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{15}\! \left(x \right)+F_{38}\! \left(x \right)
F_{52}\! \left(x \right) = F_{154}\! \left(x \right)+F_{23}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{66}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{7}\! \left(x \right)
F_{56}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \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_{62}\! \left(x \right)
F_{59}\! \left(x \right) = F_{19}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{28}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{52}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{135}\! \left(x \right)+F_{23}\! \left(x \right)+F_{68}\! \left(x \right)+F_{97}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{77}\! \left(x \right)
F_{70}\! \left(x \right) = F_{56}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{27}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{77}\! \left(x \right) = F_{67}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{79}\! \left(x \right)+F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{71}\! \left(x \right)
F_{82}\! \left(x \right) = F_{78}\! \left(x \right)
F_{83}\! \left(x \right) = 0
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_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{91}\! \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_{34}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{87}\! \left(x \right)
F_{91}\! \left(x \right) = 3 F_{23}\! \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_{75}\! \left(x \right)
F_{95}\! \left(x \right) = F_{91}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{23}\! \left(x \right)+F_{49}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{104}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)+F_{61}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{99}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{116}\! \left(x \right)+F_{23}\! \left(x \right)+F_{97}\! \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_{110}\! \left(x \right)
F_{108}\! \left(x \right) = F_{103}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{76}\! \left(x \right)
F_{110}\! \left(x \right) = F_{105}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{112}\! \left(x \right)+F_{83}\! \left(x \right)+F_{96}\! \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_{109}\! \left(x \right)
F_{115}\! \left(x \right) = F_{111}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \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_{26}\! \left(x \right)
F_{120}\! \left(x \right) = F_{117}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{122}\! \left(x \right)+F_{125}\! \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_{34}\! \left(x \right)
F_{124}\! \left(x \right) = F_{121}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{4}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \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_{41}\! \left(x \right)
F_{130}\! \left(x \right) = F_{127}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{125}\! \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_{47}\! \left(x \right)
F_{134}\! \left(x \right) = F_{131}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{150}\! \left(x \right)
F_{137}\! \left(x \right) = F_{117}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{116}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{143}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{60}\! \left(x \right)
F_{142}\! \left(x \right) = F_{76}\! \left(x \right)
F_{143}\! \left(x \right) = F_{138}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{145}\! \left(x \right)+F_{149}\! \left(x \right)+F_{96}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{4}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{148}\! \left(x \right)
F_{147}\! \left(x \right) = F_{142}\! \left(x \right)
F_{148}\! \left(x \right) = F_{144}\! \left(x \right)
F_{149}\! \left(x \right) = 0
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{152}\! \left(x \right)
F_{151}\! \left(x \right) = F_{88}\! \left(x \right)
F_{152}\! \left(x \right) = 3 F_{23}\! \left(x \right)+F_{153}\! \left(x \right)+F_{92}\! \left(x \right)
F_{153}\! \left(x \right) = F_{151}\! \left(x \right) F_{4}\! \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_{157}\! \left(x \right)
F_{156}\! \left(x \right) = F_{15}\! \left(x \right)+F_{99}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{159}\! \left(x \right)
F_{158}\! \left(x \right) = F_{118}\! \left(x \right)
F_{159}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{139}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{158}\! \left(x \right) F_{4}\! \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_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_7(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_4(x)*F_7(x))
Eq(F_14(x), F_15(x) + F_52(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_21(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_4(x))
Eq(F_21(x), F_15(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_24(x) + F_50(x))
Eq(F_23(x), 0)
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_30(x))
Eq(F_26(x), F_19(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_4(x))
Eq(F_30(x), F_22(x) + F_31(x))
Eq(F_31(x), 2*F_23(x) + F_32(x) + F_36(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_27(x))
Eq(F_35(x), F_31(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_23(x) + F_39(x) + F_49(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_43(x))
Eq(F_41(x), F_4(x) + F_42(x))
Eq(F_42(x), F_28(x))
Eq(F_43(x), F_38(x) + F_44(x))
Eq(F_44(x), 2*F_23(x) + F_36(x) + F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_42(x))
Eq(F_48(x), F_44(x))
Eq(F_49(x), F_15(x)*F_4(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_15(x) + F_38(x))
Eq(F_52(x), F_154(x) + F_23(x) + F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_66(x))
Eq(F_55(x), F_56(x) + F_7(x))
Eq(F_56(x), F_23(x) + F_28(x) + F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_62(x))
Eq(F_59(x), F_19(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_19(x)*F_4(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_28(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_63(x))
Eq(F_66(x), F_52(x) + F_67(x))
Eq(F_67(x), F_135(x) + F_23(x) + F_68(x) + F_97(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_77(x))
Eq(F_70(x), F_56(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_27(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_27(x)*F_4(x))
Eq(F_77(x), F_67(x) + F_78(x))
Eq(F_78(x), 2*F_23(x) + F_79(x) + F_83(x) + F_84(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_71(x))
Eq(F_82(x), F_78(x))
Eq(F_83(x), 0)
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_87(x) + F_91(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_34(x) + F_90(x))
Eq(F_90(x), F_87(x))
Eq(F_91(x), 3*F_23(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_75(x))
Eq(F_95(x), F_91(x))
Eq(F_96(x), F_4(x)*F_87(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x) + F_23(x) + F_49(x))
Eq(F_100(x), F_101(x)*F_4(x))
Eq(F_101(x), F_102(x) + F_104(x))
Eq(F_102(x), F_103(x) + F_4(x))
Eq(F_103(x), F_23(x) + F_28(x) + F_61(x))
Eq(F_104(x), F_105(x) + F_99(x))
Eq(F_105(x), F_106(x) + F_116(x) + F_23(x) + F_97(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_108(x) + F_110(x))
Eq(F_108(x), F_103(x) + F_109(x))
Eq(F_109(x), F_76(x))
Eq(F_110(x), F_105(x) + F_111(x))
Eq(F_111(x), F_112(x) + 2*F_23(x) + F_83(x) + F_96(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_109(x))
Eq(F_115(x), F_111(x))
Eq(F_116(x), F_117(x)*F_4(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_120(x) + F_26(x))
Eq(F_120(x), F_117(x) + F_121(x))
Eq(F_121(x), F_122(x) + F_125(x) + 2*F_23(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_124(x) + F_34(x))
Eq(F_124(x), F_121(x))
Eq(F_125(x), F_126(x)*F_4(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_130(x) + F_41(x))
Eq(F_130(x), F_127(x) + F_131(x))
Eq(F_131(x), F_125(x) + F_132(x) + 2*F_23(x))
Eq(F_132(x), F_133(x)*F_4(x))
Eq(F_133(x), F_134(x) + F_47(x))
Eq(F_134(x), F_131(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_137(x) + F_150(x))
Eq(F_137(x), F_117(x) + F_138(x))
Eq(F_138(x), F_116(x) + F_139(x) + 2*F_23(x))
Eq(F_139(x), F_140(x)*F_4(x))
Eq(F_140(x), F_141(x) + F_143(x))
Eq(F_141(x), F_142(x) + F_60(x))
Eq(F_142(x), F_76(x))
Eq(F_143(x), F_138(x) + F_144(x))
Eq(F_144(x), F_145(x) + F_149(x) + 2*F_23(x) + F_96(x))
Eq(F_145(x), F_146(x)*F_4(x))
Eq(F_146(x), F_147(x) + F_148(x))
Eq(F_147(x), F_142(x))
Eq(F_148(x), F_144(x))
Eq(F_149(x), 0)
Eq(F_150(x), F_151(x) + F_152(x))
Eq(F_151(x), F_88(x))
Eq(F_152(x), F_153(x) + 3*F_23(x) + F_92(x))
Eq(F_153(x), F_151(x)*F_4(x))
Eq(F_154(x), F_155(x)*F_4(x))
Eq(F_155(x), F_156(x) + F_157(x))
Eq(F_156(x), F_15(x) + F_99(x))
Eq(F_157(x), F_158(x) + F_159(x))
Eq(F_158(x), F_118(x))
Eq(F_159(x), F_139(x) + F_160(x) + 2*F_23(x))
Eq(F_160(x), F_158(x)*F_4(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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