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A054410 Susceptibility series H_3 for 2-dimensional Ising model (divided by 2). 6
1, 12, 52, 148, 328, 620, 1052, 1652, 2448, 3468, 4740, 6292, 8152, 10348, 12908, 15860, 19232, 23052, 27348, 32148, 37480, 43372, 49852, 56948, 64688, 73100, 82212, 92052, 102648, 114028, 126220, 139252, 153152, 167948, 183668, 200340, 217992, 236652 (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,-6,4,-1).

FORMULA

G.f.: (1+8*x+10*x^2+8*x^3+x^4) / (1-x)^4.

From Colin Barker, Dec 09 2016: (Start)

a(n) = 2*(n*(11 + 7*n^2))/3 for n>0.

a(0)=1, a(1)=12, a(2)=52, a(3)=148, a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)

MATHEMATICA

CoefficientList[Series[(1+8*x+10*x^2+8*x^3+x^4)/(1-x)^4, {x, 0, 37}], x] (* or *) a[0]=1; a[n_]:=2*(n*(11+7*n^2))/3; Table[a[n], {n, 0, 37}] (* Indranil Ghosh, Feb 24 2017 *)

PROG

(PARI) Vec((1+8*x+10*x^2+8*x^3+x^4)/(1-x)^4 + O(x^50)) \\ Colin Barker, Dec 09 2016

(Python)

def A054410(n):

....if n==0:return 1

....return 2*(n*(11 + 7*n**2))/3 # Indranil Ghosh, Feb 24 2017

CROSSREFS

Cf. A008574, A054275, A054389, A054764.

Sequence in context: A317466 A045219 A325379 * A185355 A297757 A223249

Adjacent sequences:  A054407 A054408 A054409 * A054411 A054412 A054413

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 09 2000

STATUS

approved

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Last modified June 17 19:10 EDT 2019. Contains 324198 sequences. (Running on oeis4.)