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A054410 Susceptibility series H_3 for 2-dimensional Ising model (divided by 2). 6

%I

%S 1,12,52,148,328,620,1052,1652,2448,3468,4740,6292,8152,10348,12908,

%T 15860,19232,23052,27348,32148,37480,43372,49852,56948,64688,73100,

%U 82212,92052,102648,114028,126220,139252,153152,167948,183668,200340,217992,236652

%N Susceptibility series H_3 for 2-dimensional Ising model (divided by 2).

%H Colin Barker, <a href="/A054410/b054410.txt">Table of n, a(n) for n = 0..1000</a>

%H A. J. Guttmann, <a href="http://www.ms.unimelb.edu.au/~tonyg/articles/viennafinal.pdf">Indicators of solvability for lattice models</a>, Discrete Math., 217 (2000), 167-189.

%H D. Hansel et al., <a href="http://dx.doi.org/10.1007/BF01010400">Analytical properties of the anisotropic cubic Ising model</a>, J. Stat. Phys., 48 (1987), 69-80.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

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

%F From _Colin Barker_, Dec 09 2016: (Start)

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

%F 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.

%F (End)

%t 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 *)

%o (PARI) Vec((1+8*x+10*x^2+8*x^3+x^4)/(1-x)^4 + O(x^50)) \\ _Colin Barker_, Dec 09 2016

%o (Python)

%o def A054410(n):

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

%o ....return 2*(n*(11 + 7*n**2))/3 # _Indranil Ghosh_, Feb 24 2017

%Y Cf. A008574, A054275, A054389, A054764.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, May 09 2000

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Last modified July 23 15:58 EDT 2019. Contains 325258 sequences. (Running on oeis4.)