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%I #23 Sep 08 2022 08:45:01
%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="https://doi.org/10.1016/S0012-365X(99)00262-9">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. (End)
%F E.g.f.: (3 + 2*x*(18 + 21*x + 7*x^2)*exp(x))/3. - _G. C. Greubel_, Jul 31 2019
%t 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 *)
%o (PARI) Vec((1+8*x+10*x^2+8*x^3+x^4)/(1-x)^4 + O(x^40)) \\ _Colin Barker_, Dec 09 2016
%o (PARI) vector(40, n, n--; if(n==0,1, 2*n*(11+7*n^2)/3)) \\ _G. C. Greubel_, Jul 31 2019
%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
%o (Magma) [1] cat [2*n*(11+7*n^2)/3: n in [1..40]]; // _G. C. Greubel_, Jul 31 2019
%o (Sage) [1]+[2*n*(11+7*n^2)/3 for n in (1..40)] # _G. C. Greubel_, Jul 31 2019
%o (GAP) Concatenation([1], List([1..40], n-> 2*n*(11+7*n^2)/3)); # _G. C. Greubel_, Jul 31 2019
%Y Cf. A008574, A054275, A054389, A054764.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, May 09 2000
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