0123_0231_1320_3021
Counting sequence:
1, 1, 2, 6, 20, 61, 164, 419, 1052, 2631, 6584, 16504, 41445, 104271, 262871, 664239, 1682763, 4274900, 10891344, 27828903, 71308170, 183210787, 471900222, 1218266900, 3151572355, 8167766251, 21201777549, 55111456459, 143425848457, 373639358736, 974203889494, 2541909097459, 6636390349240, 17334915472511, 45299368150276, 118416354777504, 309637774175393, 809835542777495, 2118468694810339, 5542611309177623, 14503120350264455, 37953589961810332, 99329955586030652, 259978071399474095, 680482075382741990, 1781211968539466091, 4662617268561286634, 12205517235772418524, 31951588080942277887, 83644347583241027091, 218971233608688978329, 573248049105526099539, 1500728546214685281285, 3928845265746168625976, 10285615285089703904706, 26927601739480944062619, 70496361833971645505748, 184559765639176150581415, 483179372736251556145584, 1264970971169789257580168, 3311718255555980921097565, 8670152162214370855312927, 22698672802791745206237807, 59425730994056855572625215, 155578240740029142427060675, 407308414188817515981601956, 1066345810858509146644773544, 2791726561510983606761765239, 7308828807737350431154859842, 19134749420843921967096547571, 50095397945890825524797544214, 131151400126196033630662598244, 343358711268888063094586104955, 898924546113974414174374823291, 2353414541314723110014394906661, 6161318284767773698947766754459, 16130538683181865586442600909953, 42230294416619986705801579392160, 110560337690912495472758706049454, 289450704540964082415104994940163, 757791746964983745850152537878000, 1983924476927727334703737249458447, 5193981561943364068361255535342812, 13598019959032509528781361809395760, 35600077803022964183735545757845785, 93202212400688771596927151819082471, 244006557249573243332235237071718779, 638817454946332049182913734290781479, 1672445798578089844809060097540680447, 4378519922344565181203483869013725676, 11463113930717777313711127191872389524, 30010821792611599622618137126565747199, 78569351289240980919029631004595790750, 205697231752318477890807849207274854331, 538522343307892411814286230095995427266, 1409869796822932569760450376646840228524, 3691087044405869740037451098056524155383, 9663391330767001231760564187831313368355, 25299086936402098630518770993273946502449, 66233869454972903275102080301002727192483, 173402521380613283434600394792237723941885
Generating function in Maple syntax:
(8*x^12-63*x^11+184*x^10-243*x^9+121*x^8+79*x^7-251*x^6+351*x^5-315*x^4+179*x^3-62*x^2+12*x-1)/(x^2-3*x+1)/(2*x-1)^3/(x-1)^4
Generating function in latex syntax:
\frac{8 x^{12}-63 x^{11}+184 x^{10}-243 x^{9}+121 x^{8}+79 x^{7}-251 x^{6}+351 x^{5}-315 x^{4}+179 x^{3}-62 x^{2}+12 x -1}{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{3} \left(x -1\right)^{4}}
Generating function in sympy syntax:
(8*x**12 - 63*x**11 + 184*x**10 - 243*x**9 + 121*x**8 + 79*x**7 - 251*x**6 + 351*x**5 - 315*x**4 + 179*x**3 - 62*x**2 + 12*x - 1)/((x - 1)**4*(2*x - 1)**3*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(x^2-3*x+1)*(2*x-1)^3*(x-1)^4*F(x)+8*x^12-63*x^11+184*x^10-243*x^9+121*x^8+79*x^7-251*x^6+351*x^5-315*x^4+179*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(2 x -1\right)^{3} \left(x -1\right)^{4} F \! \left(x \right)+8 x^{12}-63 x^{11}+184 x^{10}-243 x^{9}+121 x^{8}+79 x^{7}-251 x^{6}+351 x^{5}-315 x^{4}+179 x^{3}-62 x^{2}+12 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,-47/8,n = 1,-31/16,n = 2,5/8,n = 3,1,0)+1/960*(-96*5^(1/2)+480)*(3/2-1/2*5^(1/2))^(-n)+1/960*(96*5^(1/2)+480)*(3/2+1/2*5^(1/2))^(-n)+1/960*(15*n^2+75*n-120)*2^n+1/6*n^3-25/6*n+6
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}-\frac{47}{8} & n =0 \\ -\frac{31}{16} & n =1 \\ \frac{5}{8} & n =2 \\ 1 & n =3 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{\left(-96 \sqrt{5}+480\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{960}+\frac{\left(96 \sqrt{5}+480\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{960}+\frac{\left(15 n^{2}+75 n -120\right) 2^{n}}{960}+\frac{n^{3}}{6}-\frac{25 n}{6}+6
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 61
a(6) = 164
a(7) = 419
a(8) = 1052
a(9) = 2631
a(10) = 6584
a(11) = 16504
a(12) = 41445
a(n+5) = 1/6*n^3-n^2+8*a(n)-36*a(n+1)+50*a(n+2)-31*a(n+3)+9*a(n+4)-37/6*n+18, n >= 13
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) = 61
a \! \left(6\right) = 164
a \! \left(7\right) = 419
a \! \left(8\right) = 1052
a \! \left(9\right) = 2631
a \! \left(10\right) = 6584
a \! \left(11\right) = 16504
a \! \left(12\right) = 41445
a \! \left(n +5\right) = \frac{n^{3}}{6}-n^{2}+8 a \! \left(n \right)-36 a \! \left(n +1\right)+50 a \! \left(n +2\right)-31 a \! \left(n +3\right)+9 a \! \left(n +4\right)-\frac{37 n}{6}+18, \quad n \geq 13
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15032/
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[29,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[24,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[4,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[4,x]
F[23,x] = F[19,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[11,x]
F[28,x] = F[24,x]
F[29,x] = F[30,x]+F[66,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[1,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[17,x]*F[4,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = F[38,x]+F[39,x]+F[64,x]
F[38,x] = 0
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[34,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[22,x]*F[4,x]
F[44,x] = F[37,x]+F[45,x]
F[45,x] = 2*F[38,x]+F[46,x]+F[50,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[42,x]
F[49,x] = F[45,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[38,x]+F[53,x]+F[63,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[57,x]
F[55,x] = F[4,x]+F[56,x]
F[56,x] = F[43,x]
F[57,x] = F[52,x]+F[58,x]
F[58,x] = 2*F[38,x]+F[50,x]+F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[56,x]
F[62,x] = F[58,x]
F[63,x] = F[30,x]*F[4,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[30,x]+F[52,x]
F[66,x] = F[184,x]+F[38,x]+F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[82,x]
F[69,x] = F[7,x]+F[70,x]
F[70,x] = F[38,x]+F[71,x]+F[76,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[11,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[4,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[78,x]+F[81,x]
F[78,x] = F[34,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[27,x]*F[4,x]
F[81,x] = F[43,x]
F[82,x] = F[66,x]+F[83,x]
F[83,x] = F[135,x]+F[175,x]+F[38,x]+F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]+F[92,x]
F[86,x] = F[70,x]+F[87,x]
F[87,x] = 2*F[38,x]+F[88,x]+F[90,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[73,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[42,x]
F[92,x] = F[83,x]+F[93,x]
F[93,x] = 2*F[38,x]+F[130,x]+F[94,x]+F[98,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[96,x]+F[97,x]
F[96,x] = F[87,x]
F[97,x] = F[93,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]
F[100,x] = 2*F[38,x]+F[101,x]+F[118,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]+F[107,x]
F[103,x] = F[104,x]+F[73,x]
F[104,x] = 2*F[38,x]+F[105,x]+F[88,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[56,x]
F[107,x] = F[100,x]+F[108,x]
F[108,x] = 2*F[38,x]+F[109,x]+F[113,x]+F[98,x]
F[109,x] = F[110,x]*F[4,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[104,x]
F[112,x] = F[108,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[4,x]
F[116,x] = F[117,x]+F[61,x]
F[117,x] = F[115,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]
F[121,x] = F[122,x]*F[4,x]
F[122,x] = F[123,x]+F[55,x]
F[123,x] = F[120,x]+F[124,x]
F[124,x] = 2*F[38,x]+F[125,x]+F[128,x]
F[125,x] = F[126,x]*F[4,x]
F[126,x] = F[127,x]+F[61,x]
F[127,x] = F[124,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[120,x]
F[130,x] = F[131,x]*F[4,x]
F[131,x] = F[132,x]
F[132,x] = F[133,x]*F[4,x]
F[133,x] = F[134,x]+F[48,x]
F[134,x] = F[132,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[100,x]+F[137,x]
F[137,x] = F[138,x]+F[172,x]+F[38,x]
F[138,x] = F[139,x]*F[4,x]
F[139,x] = F[140,x]+F[145,x]
F[140,x] = F[11,x]+F[141,x]
F[141,x] = F[142,x]+F[38,x]+F[71,x]
F[142,x] = F[143,x]*F[4,x]
F[143,x] = F[144,x]+F[34,x]
F[144,x] = F[43,x]
F[145,x] = F[137,x]+F[146,x]
F[146,x] = F[135,x]+F[147,x]+F[161,x]+F[38,x]
F[147,x] = F[148,x]*F[4,x]
F[148,x] = F[149,x]+F[153,x]
F[149,x] = F[141,x]+F[150,x]
F[150,x] = 2*F[38,x]+F[151,x]+F[88,x]
F[151,x] = F[152,x]*F[4,x]
F[152,x] = F[42,x]
F[153,x] = F[146,x]+F[154,x]
F[154,x] = 2*F[38,x]+F[155,x]+F[159,x]+F[98,x]
F[155,x] = F[156,x]*F[4,x]
F[156,x] = F[157,x]+F[158,x]
F[157,x] = F[150,x]
F[158,x] = F[154,x]
F[159,x] = F[160,x]*F[4,x]
F[160,x] = F[132,x]
F[161,x] = F[162,x]*F[4,x]
F[162,x] = F[163,x]+F[171,x]
F[163,x] = F[164,x]
F[164,x] = F[165,x]*F[4,x]
F[165,x] = F[166,x]+F[41,x]
F[166,x] = F[163,x]+F[167,x]
F[167,x] = 2*F[38,x]+F[128,x]+F[168,x]
F[168,x] = F[169,x]*F[4,x]
F[169,x] = F[170,x]+F[48,x]
F[170,x] = F[167,x]
F[171,x] = F[115,x]
F[172,x] = F[173,x]*F[4,x]
F[173,x] = F[174,x]+F[30,x]
F[174,x] = F[121,x]
F[175,x] = F[176,x]*F[4,x]
F[176,x] = F[177,x]+F[183,x]
F[177,x] = F[163,x]+F[178,x]
F[178,x] = F[179,x]
F[179,x] = F[180,x]*F[4,x]
F[180,x] = F[181,x]+F[182,x]
F[181,x] = F[79,x]
F[182,x] = F[178,x]
F[183,x] = F[132,x]
F[184,x] = F[185,x]*F[4,x]
F[185,x] = F[186,x]+F[187,x]
F[186,x] = F[137,x]+F[30,x]
F[187,x] = F[188,x]+F[189,x]
F[188,x] = F[164,x]
F[189,x] = F[179,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_{29}\! \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_{24}\! \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_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \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_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{66}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{1}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)+F_{64}\! \left(x \right)
F_{38}\! \left(x \right) = 0
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_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{37}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{46}\! \left(x \right)+F_{50}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{42}\! \left(x \right)
F_{49}\! \left(x \right) = F_{45}\! \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_{52}\! \left(x \right) = F_{38}\! \left(x \right)+F_{53}\! \left(x \right)+F_{63}\! \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_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{43}\! \left(x \right)
F_{57}\! \left(x \right) = F_{52}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{50}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{56}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)
F_{63}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{30}\! \left(x \right)+F_{52}\! \left(x \right)
F_{66}\! \left(x \right) = F_{184}\! \left(x \right)+F_{38}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{82}\! \left(x \right)
F_{69}\! \left(x \right) = F_{7}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{38}\! \left(x \right)+F_{71}\! \left(x \right)+F_{76}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \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_{4}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{81}\! \left(x \right)
F_{78}\! \left(x \right) = F_{34}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{81}\! \left(x \right) = F_{43}\! \left(x \right)
F_{82}\! \left(x \right) = F_{66}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{135}\! \left(x \right)+F_{175}\! \left(x \right)+F_{38}\! \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_{92}\! \left(x \right)
F_{86}\! \left(x \right) = F_{70}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{73}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{42}\! \left(x \right)
F_{92}\! \left(x \right) = F_{83}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{130}\! \left(x \right)+F_{94}\! \left(x \right)+F_{98}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{97}\! \left(x \right)
F_{96}\! \left(x \right) = F_{87}\! \left(x \right)
F_{97}\! \left(x \right) = F_{93}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{101}\! \left(x \right)+F_{118}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{107}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{73}\! \left(x \right)
F_{104}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{105}\! \left(x \right)+F_{88}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{56}\! \left(x \right)
F_{107}\! \left(x \right) = F_{100}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{109}\! \left(x \right)+F_{113}\! \left(x \right)+F_{98}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{4}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{104}\! \left(x \right)
F_{112}\! \left(x \right) = F_{108}\! \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_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{61}\! \left(x \right)
F_{117}\! \left(x \right) = F_{115}\! \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_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{4}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{55}\! \left(x \right)
F_{123}\! \left(x \right) = F_{120}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{125}\! \left(x \right)+F_{128}\! \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_{61}\! \left(x \right)
F_{127}\! \left(x \right) = F_{124}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = F_{120}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{4}\! \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_{48}\! \left(x \right)
F_{134}\! \left(x \right) = F_{132}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{100}\! \left(x \right)+F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{172}\! \left(x \right)+F_{38}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{4}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{145}\! \left(x \right)
F_{140}\! \left(x \right) = F_{11}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{38}\! \left(x \right)+F_{71}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{34}\! \left(x \right)
F_{144}\! \left(x \right) = F_{43}\! \left(x \right)
F_{145}\! \left(x \right) = F_{137}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{135}\! \left(x \right)+F_{147}\! \left(x \right)+F_{161}\! \left(x \right)+F_{38}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{4}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{153}\! \left(x \right)
F_{149}\! \left(x \right) = F_{141}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{151}\! \left(x \right)+F_{88}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{4}\! \left(x \right)
F_{152}\! \left(x \right) = F_{42}\! \left(x \right)
F_{153}\! \left(x \right) = F_{146}\! \left(x \right)+F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{155}\! \left(x \right)+F_{159}\! \left(x \right)+F_{98}\! \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_{158}\! \left(x \right)
F_{157}\! \left(x \right) = F_{150}\! \left(x \right)
F_{158}\! \left(x \right) = F_{154}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right) F_{4}\! \left(x \right)
F_{160}\! \left(x \right) = F_{132}\! \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_{171}\! \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_{41}\! \left(x \right)
F_{166}\! \left(x \right) = F_{163}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{128}\! \left(x \right)+F_{168}\! \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_{48}\! \left(x \right)
F_{170}\! \left(x \right) = F_{167}\! \left(x \right)
F_{171}\! \left(x \right) = F_{115}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right) F_{4}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)+F_{30}\! \left(x \right)
F_{174}\! \left(x \right) = F_{121}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right) F_{4}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{183}\! \left(x \right)
F_{177}\! \left(x \right) = F_{163}\! \left(x \right)+F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right) F_{4}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{182}\! \left(x \right)
F_{181}\! \left(x \right) = F_{79}\! \left(x \right)
F_{182}\! \left(x \right) = F_{178}\! \left(x \right)
F_{183}\! \left(x \right) = F_{132}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right) F_{4}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{187}\! \left(x \right)
F_{186}\! \left(x \right) = F_{137}\! \left(x \right)+F_{30}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)+F_{189}\! \left(x \right)
F_{188}\! \left(x \right) = F_{164}\! \left(x \right)
F_{189}\! \left(x \right) = F_{179}\! \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_29(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_24(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_4(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_4(x))
Eq(F_23(x), F_19(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_11(x))
Eq(F_28(x), F_24(x))
Eq(F_29(x), F_30(x) + F_66(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_1(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_17(x)*F_4(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), F_38(x) + F_39(x) + F_64(x))
Eq(F_38(x), 0)
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_34(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_22(x)*F_4(x))
Eq(F_44(x), F_37(x) + F_45(x))
Eq(F_45(x), 2*F_38(x) + F_46(x) + F_50(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_42(x))
Eq(F_49(x), F_45(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_38(x) + F_53(x) + F_63(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_57(x))
Eq(F_55(x), F_4(x) + F_56(x))
Eq(F_56(x), F_43(x))
Eq(F_57(x), F_52(x) + F_58(x))
Eq(F_58(x), 2*F_38(x) + F_50(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_56(x))
Eq(F_62(x), F_58(x))
Eq(F_63(x), F_30(x)*F_4(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_30(x) + F_52(x))
Eq(F_66(x), F_184(x) + F_38(x) + F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_82(x))
Eq(F_69(x), F_7(x) + F_70(x))
Eq(F_70(x), F_38(x) + F_71(x) + F_76(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_11(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_4(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_81(x))
Eq(F_78(x), F_34(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_27(x)*F_4(x))
Eq(F_81(x), F_43(x))
Eq(F_82(x), F_66(x) + F_83(x))
Eq(F_83(x), F_135(x) + F_175(x) + F_38(x) + F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_92(x))
Eq(F_86(x), F_70(x) + F_87(x))
Eq(F_87(x), 2*F_38(x) + F_88(x) + F_90(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_73(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_42(x))
Eq(F_92(x), F_83(x) + F_93(x))
Eq(F_93(x), F_130(x) + 2*F_38(x) + F_94(x) + F_98(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_96(x) + F_97(x))
Eq(F_96(x), F_87(x))
Eq(F_97(x), F_93(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x) + F_118(x) + 2*F_38(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x) + F_107(x))
Eq(F_103(x), F_104(x) + F_73(x))
Eq(F_104(x), F_105(x) + 2*F_38(x) + F_88(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_56(x))
Eq(F_107(x), F_100(x) + F_108(x))
Eq(F_108(x), F_109(x) + F_113(x) + 2*F_38(x) + F_98(x))
Eq(F_109(x), F_110(x)*F_4(x))
Eq(F_110(x), F_111(x) + F_112(x))
Eq(F_111(x), F_104(x))
Eq(F_112(x), F_108(x))
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_4(x))
Eq(F_116(x), F_117(x) + F_61(x))
Eq(F_117(x), F_115(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))
Eq(F_121(x), F_122(x)*F_4(x))
Eq(F_122(x), F_123(x) + F_55(x))
Eq(F_123(x), F_120(x) + F_124(x))
Eq(F_124(x), F_125(x) + F_128(x) + 2*F_38(x))
Eq(F_125(x), F_126(x)*F_4(x))
Eq(F_126(x), F_127(x) + F_61(x))
Eq(F_127(x), F_124(x))
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_120(x))
Eq(F_130(x), F_131(x)*F_4(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_48(x))
Eq(F_134(x), F_132(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_100(x) + F_137(x))
Eq(F_137(x), F_138(x) + F_172(x) + F_38(x))
Eq(F_138(x), F_139(x)*F_4(x))
Eq(F_139(x), F_140(x) + F_145(x))
Eq(F_140(x), F_11(x) + F_141(x))
Eq(F_141(x), F_142(x) + F_38(x) + F_71(x))
Eq(F_142(x), F_143(x)*F_4(x))
Eq(F_143(x), F_144(x) + F_34(x))
Eq(F_144(x), F_43(x))
Eq(F_145(x), F_137(x) + F_146(x))
Eq(F_146(x), F_135(x) + F_147(x) + F_161(x) + F_38(x))
Eq(F_147(x), F_148(x)*F_4(x))
Eq(F_148(x), F_149(x) + F_153(x))
Eq(F_149(x), F_141(x) + F_150(x))
Eq(F_150(x), F_151(x) + 2*F_38(x) + F_88(x))
Eq(F_151(x), F_152(x)*F_4(x))
Eq(F_152(x), F_42(x))
Eq(F_153(x), F_146(x) + F_154(x))
Eq(F_154(x), F_155(x) + F_159(x) + 2*F_38(x) + F_98(x))
Eq(F_155(x), F_156(x)*F_4(x))
Eq(F_156(x), F_157(x) + F_158(x))
Eq(F_157(x), F_150(x))
Eq(F_158(x), F_154(x))
Eq(F_159(x), F_160(x)*F_4(x))
Eq(F_160(x), F_132(x))
Eq(F_161(x), F_162(x)*F_4(x))
Eq(F_162(x), F_163(x) + F_171(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_41(x))
Eq(F_166(x), F_163(x) + F_167(x))
Eq(F_167(x), F_128(x) + F_168(x) + 2*F_38(x))
Eq(F_168(x), F_169(x)*F_4(x))
Eq(F_169(x), F_170(x) + F_48(x))
Eq(F_170(x), F_167(x))
Eq(F_171(x), F_115(x))
Eq(F_172(x), F_173(x)*F_4(x))
Eq(F_173(x), F_174(x) + F_30(x))
Eq(F_174(x), F_121(x))
Eq(F_175(x), F_176(x)*F_4(x))
Eq(F_176(x), F_177(x) + F_183(x))
Eq(F_177(x), F_163(x) + F_178(x))
Eq(F_178(x), F_179(x))
Eq(F_179(x), F_180(x)*F_4(x))
Eq(F_180(x), F_181(x) + F_182(x))
Eq(F_181(x), F_79(x))
Eq(F_182(x), F_178(x))
Eq(F_183(x), F_132(x))
Eq(F_184(x), F_185(x)*F_4(x))
Eq(F_185(x), F_186(x) + F_187(x))
Eq(F_186(x), F_137(x) + F_30(x))
Eq(F_187(x), F_188(x) + F_189(x))
Eq(F_188(x), F_164(x))
Eq(F_189(x), F_179(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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