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A007900 Coordination sequence for D_4 lattice.

%I A007900 #28 Dec 10 2023 16:00:12
%S A007900 1,24,144,456,1056,2040,3504,5544,8256,11736,16080,21384,27744,35256,
%T A007900 44016,54120,65664,78744,93456,109896,128160,148344,170544,194856,
%U A007900 221376,250200,281424,315144,351456
%N A007900 Coordination sequence for D_4 lattice.
%D A007900 M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
%H A007900 M. Baake and U. Grimm, <a href="https://arxiv.org/abs/cond-mat/9706122">Coordination sequences for root lattices and related graphs</a>, arXiv:cond-mat/9706122, Zeit. f. Kristallographie, 212 (1997), 253-256.
%H A007900 R. Bacher, P. de la Harpe and B. Venkov, <a href="http://dx.doi.org/10.1016/S0764-4442(97)83542-2">Séries de croissance et séries d'Ehrhart associées aux réseaux de racines</a>, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
%H A007900 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).
%H A007900 M. O'Keeffe, <a href="http://dx.doi.org/10.1524/zkri.1995.210.12.905">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908.
%H A007900 M. O'Keeffe, <a href="/A008527/a008527.pdf">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
%H A007900 <a href="/index/Da#D4">Index entries for sequences related to D_4 lattice</a>
%H A007900 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).
%F A007900 G.f.: (1+54*x^2+20*x+20*x^3+x^4)/(1-x)^4 = 1+24*x*(x+1)^2/(x-1)^4.
%F A007900 G.f. for coordination sequence of D_n lattice: (Sum(binomial(2*n, 2*i)*z^i, i=0..n)-2*n*z*(1+z)^(n-2))/(1-z)^n.
%p A007900 if n=0 then 1 else 8*n*(2*n^2+1); fi;
%Y A007900 A row of array A103903.
%K A007900 nonn,easy
%O A007900 0,2
%A A007900 _N. J. A. Sloane_ and _J. H. Conway_