A055857 Susceptibility series H_6 for 2-dimensional Ising model (divided by 2).
1, 24, 200, 1052, 3994, 12292, 32088, 74320, 155986, 303512, 553520, 958636, 1586554, 2529708, 3900872, 5848984, 8548370, 12224144, 17131328, 23593828, 31968890, 42705180, 56285952, 73313624, 94423970, 120405112, 152074032, 190440188, 236532474, 291620356
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- A. J. Guttmann and I. G. Enting, Solvability of some statistical mechanical systems, Phys. Rev. Lett., 76 (1996), 344-347.
- Index entries for linear recurrences with constant coefficients, signature (-1,4,7,-3,-18,-11,19,29,0,-29,-19,11,18,3,-7,-4,1,1).
Programs
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Mathematica
CoefficientList[Series[(1+25*x+220*x^2+1149*x^3+4081*x^4+10768*x^5+22083*x^6 +36283*x^7+48543*x^8+53446*x^9+48543*x^10+36283*x^11+22083*x^12+10768*x^13 + 4081*x^14+1149*x^15+220*x^16+25*x^17+x^18)/((1+x)*(1-x^2)^4*(1-x^3)^3), {x,0, 30}], x] (* G. C. Greubel, Jan 17 2020 *) -
PARI
Vec((1 +25*x +220*x^2 +1149*x^3 +4081*x^4 +10768*x^5 +22083*x^6 +36283*x^7 +48543*x^8 +53446*x^9 +48543*x^10 +36283*x^11 +22083*x^12 +10768*x^13 +4081*x^14 +1149*x^15 +220*x^16 +25*x^17 +x^18) / ((1 -x)^7*(1 +x)^5*(1 +x +x^2)^3) + O(x^50)) \\ Colin Barker, Dec 10 2016
Formula
G.f.: (1+x^18+25*(x+x^17)+220*(x^2+x^16)+1149*(x^3+x^15)+ 4081*(x^4+x^14)+10768*(x^5+x^13)+22083*(x^6+x^12)+36283*(x^7+x^11)+ 48543*(x^8+x^10)+53446*x^9) / (((1-x^3)^3)*(1-x)^4*(1+x)^5).