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A054389 Susceptibility series H_5 for 2-dimensional Ising model (divided by 2). 6
1, 20, 140, 620, 2016, 5364, 12292, 25228, 47488, 83508, 138908, 220748, 337568, 499668, 719124, 1010092, 1388800, 1873876, 2486316, 3249836, 4190816, 5338676, 6725796, 8387916, 10364032, 12696820, 15432508, 18621324, 22317344, 26578964, 31468724, 37053804 (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 (4,-4,-4,10,-4,-4,4,-1).

FORMULA

G.f.: (1 + 16*x + 64*x^2 + 144*x^3 + 166*x^4 + 144*x^5 + 64*x^6 + 16*x^7 + x^8) / ((1 - x)^6*(1 + x)^2).

From Colin Barker, Dec 09 2016: (Start)

a(n) = 4*a(n-1) - 4*a(n-2) - 4*a(n-3) + 10*a(n-4) - 4*a(n-5) - 4*a(n-6) + 4*a(n-7) - a(n-8) for n>8.

a(n) = (77*n^5 + 630*n^3 + 448*n)/60 for n>0 and even.

a(n) = (77*n^5 + 630*n^3 + 493*n)/60 for n odd.

(End)

MATHEMATICA

LinearRecurrence[{4, -4, -4, 10, -4, -4, 4, -1}, {1, 20, 140, 620, 2016, 5364, 12292, 25228, 47488}, 32] (* or *) CoefficientList[Series[(1 + 16*x + 64*x^2 + 144*x^3 + 166*x^4 + 144*x^5 + 64*x^6 + 16*x^7 + x^8) / ((1 - x)^6*(1 + x)^2) , {x, 0, 31}], x] (* Indranil Ghosh, Feb 24 2017 *)

PROG

(PARI) Vec((1 + 16*x + 64*x^2 + 144*x^3 + 166*x^4 + 144*x^5 + 64*x^6 + 16*x^7 + x^8) / ((1 - x)^6*(1 + x)^2) + O(x^30)) \\ Colin Barker, Dec 09 2016

CROSSREFS

Cf. A008574, A054275, A054410, A054764.

Sequence in context: A236988 A134382 A105939 * A253003 A293932 A071816

Adjacent sequences:  A054386 A054387 A054388 * A054390 A054391 A054392

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 09 2000

STATUS

approved

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Last modified June 18 07:06 EDT 2019. Contains 324203 sequences. (Running on oeis4.)