A055920 Susceptibility series H_4 for 2-dimensional Ising model (divided by 2) for 1 particle excitation.

1, 16, 90, 328, 886, 2016, 3986, 7208, 12050, 19096, 28802, 41936, 59030, 81048, 108586, 142816, 184386, 234688, 294410, 365176, 447702, 543856, 654370, 781368, 925586, 1089416, 1273586, 1480768, 1711670, 1969256, 2254202, 2569776, 2916610, 3298288, 3715386

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

A. J. Guttmann, Indicators of solvability for lattice models, Discrete Math., 217 (2000), 167-189 (H_4(1)/2 of Section 3).

Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

Formula

G.f.: (1 +14*x +56*x^2 +122*x^3 +146*x^4 +122*x^5 +56*x^6 +14*x^7 +x^8) / ((1 -x)^5*(1 +x)^3).

From Colin Barker, Dec 10 2016: (Start)

a(n) = (133*n^4 + 524*n^2 + 96)/48 for n>0 and even.

a(n) = (133*n^4 + 542*n^2 + 93)/48 for n odd.

(End)

Mathematica

LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {1, 16, 90, 328, 886, 2016, 3986, 7208, 12050}, 40] (* Harvey P. Dale, Oct 08 2017 *)

Prog

(PARI) Vec((1 +14*x +56*x^2 +122*x^3 +146*x^4 +122*x^5 +56*x^6 +14*x^7 +x^8)/((1 -x)^5*(1 +x)^3) + O(x^50)) \\ Colin Barker, Dec 10 2016

Crossrefs

1/2 of column 4 of A055921.

Sequence in context: A192129 A253131 A119771 * A055856 A195591 A240292

Adjacent sequences: A055917 A055918 A055919 * A055921 A055922 A055923

Keyword

nonn,easy

Author

Christian G. Bower, Jun 19 2000

Status

approved