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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)

E.g.f.: (3 + 2*x*(18 + 21*x + 7*x^2)*exp(x))/3. - G. C. Greubel, Jul 31 2019

MATHEMATICA

CoefficientList[Series[(1+8*x+10*x^2+8*x^3+x^4)/(1-x)^4, {x, 0, 40}], x] (* or *) a[0]=1; a[n_]:= 2*n*(11+7*n^2)/3; Table[a[n], {n, 0, 40}] (* Indranil Ghosh, Feb 24 2017 *)

PROG

(PARI) Vec((1+8*x+10*x^2+8*x^3+x^4)/(1-x)^4 + O(x^40)) \\ Colin Barker, Dec 09 2016

(PARI) vector(40, n, n--; if(n==0, 1, 2*n*(11+7*n^2)/3)) \\ G. C. Greubel, Jul 31 2019

(Python)

def A054410(n):

    if n == 0: return 1

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

(MAGMA) [1] cat [2*n*(11+7*n^2)/3: n in [1..40]]; // G. C. Greubel, Jul 31 2019

(Sage) [1]+[2*n*(11+7*n^2)/3 for n in (1..40)] # G. C. Greubel, Jul 31 2019

(GAP) Concatenation([1], List([1..40], n-> 2*n*(11+7*n^2)/3)); # G. C. Greubel, Jul 31 2019

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 July 5 20:10 EDT 2020. Contains 335473 sequences. (Running on oeis4.)