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A054275 Susceptibility series H_2 for 2-dimensional Ising model (divided by 2). 6

%I

%S 1,8,24,52,90,140,200,272,354,448,552,668,794,932,1080,1240,1410,1592,

%T 1784,1988,2202,2428,2664,2912,3170,3440,3720,4012,4314,4628,4952,

%U 5288,5634,5992,6360,6740,7130,7532,7944,8368,8802,9248,9704,10172,10650,11140

%N Susceptibility series H_2 for 2-dimensional Ising model (divided by 2).

%H Colin Barker, <a href="/A054275/b054275.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 (2,0,-2,1).

%F G.f.: (1+6*x+8*x^2+6*x^3+x^4) / ((1-x)^3*(1+x)).

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

%F a(n) = (11*n^2+4)/2 for n>0 and even.

%F a(n) = (11*n^2+5)/2 for n odd.

%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.

%F (End)

%t CoefficientList[Series[(1+6*x+8*x^2+6*x^3+x^4) / ((1-x)^3*(1+x)),{x,0,45}],x] (* or *) LinearRecurrence[{2,0,-2,1},{1,8,24,52,90},46] (* _Indranil Ghosh_, Feb 24 2017 *)

%o (PARI) Vec((1+6*x+8*x^2+6*x^3+x^4) / ((1-x)^3*(1+x)) + O(x^60)) \\ _Colin Barker_, Dec 09 2016

%o (PARI) a(n)=if(n, 11*n^2+5, 2)\2 \\ _Charles R Greathouse IV_, Feb 24 2017

%Y Cf. A008574, A054410, A054389, A054764.

%K nonn,easy

%O 0,2

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

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Last modified July 15 14:28 EDT 2019. Contains 325031 sequences. (Running on oeis4.)