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A008355 Coordination sequence for D_5 lattice.

%I A008355 #32 Dec 13 2023 11:02:27
%S A008355 1,40,370,1640,4930,11752,24050,44200,75010,119720,182002,265960,
%T A008355 376130,517480,695410,915752,1184770,1509160,1896050,2353000,2888002,
%U A008355 3509480,4226290,5047720,5983490,7043752
%N A008355 Coordination sequence for D_5 lattice.
%H A008355 Vincenzo Librandi, <a href="/A008355/b008355.txt">Table of n, a(n) for n = 0..1000</a>
%H A008355 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 A008355 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 A008355 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 A008355 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 A008355 M. O'Keeffe, <a href="/A008527/a008527.pdf">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
%H A008355 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).
%F A008355 a(n) = 2*(9*n^2+1)*(n^2+1) (see MAPLE line).
%F A008355 G.f.: (1+x)*(1+34*x+146*x^2+34*x^3+x^4)/(1-x)^5. [_Colin Barker_, Apr 14 2012]
%p A008355 2*(9*n^2+1)*(n^2+1);
%t A008355 CoefficientList[Series[(1+x)*(1+34*x+146*x^2+34*x^3+x^4)/(1-x)^5,{x,0,30}],x] (* _Vincenzo Librandi_, Apr 16 2012 *)
%o A008355 (Magma) [1]cat[2*(9*n^2+1)*(n^2+1): n in [1..30]]; // _Vincenzo Librandi_, Apr 16 2012
%Y A008355 A row of array A103903.
%K A008355 nonn,easy
%O A008355 0,2
%A A008355 _N. J. A. Sloane_ and _J. H. Conway_