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A054275 Susceptibility series H_2 for 2-dimensional Ising model (divided by 2). 6
1, 8, 24, 52, 90, 140, 200, 272, 354, 448, 552, 668, 794, 932, 1080, 1240, 1410, 1592, 1784, 1988, 2202, 2428, 2664, 2912, 3170, 3440, 3720, 4012, 4314, 4628, 4952, 5288, 5634, 5992, 6360, 6740, 7130, 7532, 7944, 8368, 8802, 9248, 9704, 10172, 10650, 11140 (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.

D. Hansel et al., Analytical properties of the anisotropic cubic Ising model, J. Stat. Phys., 48 (1987), 69-80.

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

FORMULA

G.f.: (1+6*x+8*x^2+6*x^3+x^4) / ((1-x)^3*(1+x)).

From Colin Barker, Dec 09 2016: (Start)

a(n) = (11*n^2+4)/2 for n>0 and even.

a(n) = (11*n^2+5)/2 for n odd.

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.

(End)

MATHEMATICA

CoefficientList[Series[(1+6*x+8*x^2+6*x^3+x^4) / ((1-x)^3*(1+x)), {x, 0, 45}], x] (* or *) LinearRecurrence[{2, 0, -2, 1}, {1, 8, 24, 52, 90}, 46] (* Indranil Ghosh, Feb 24 2017 *)

PROG

(PARI) Vec((1+6*x+8*x^2+6*x^3+x^4) / ((1-x)^3*(1+x)) + O(x^60)) \\ Colin Barker, Dec 09 2016

(PARI) a(n)=if(n, 11*n^2+5, 2)\2 \\ Charles R Greathouse IV, Feb 24 2017

CROSSREFS

Cf. A008574, A054410, A054389, A054764.

Sequence in context: A068857 A064225 A304844 * A256857 A122655 A280231

Adjacent sequences:  A054272 A054273 A054274 * A054276 A054277 A054278

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 09 2000

STATUS

approved

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)