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

0,2

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).

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).

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 *)

Prog

(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

Crossrefs

Cf. A054275, A054389, A054410, A054764, A055856.

Sequence in context: A225296 A048355 A132458 * A239574 A223748 A269691

Adjacent sequences: A055854 A055855 A055856 * A055858 A055859 A055860

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 07 2000

Status

approved