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A055920 Susceptibility series H_4 for 2-dimensional Ising model (divided by 2) for 1 particle excitation. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 23 18:54 EST 2019. Contains 320438 sequences. (Running on oeis4.)