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 A054389 Susceptibility series H_5 for 2-dimensional Ising model (divided by 2). 6

%I

%S 1,20,140,620,2016,5364,12292,25228,47488,83508,138908,220748,337568,

%T 499668,719124,1010092,1388800,1873876,2486316,3249836,4190816,

%U 5338676,6725796,8387916,10364032,12696820,15432508,18621324,22317344,26578964,31468724,37053804

%N Susceptibility series H_5 for 2-dimensional Ising model (divided by 2).

%H Colin Barker, <a href="/A054389/b054389.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_08">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-4,10,-4,-4,4,-1).

%F 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).

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

%F 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.

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

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

%F (End)

%t 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 *)

%o (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

%Y Cf. A008574, A054275, A054410, A054764.

%K nonn,easy

%O 0,2

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

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Last modified July 17 20:45 EDT 2019. Contains 325109 sequences. (Running on oeis4.)