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A008357 Coordination sequence for D_6 lattice.

%I A008357 #29 Dec 13 2023 11:05:18
%S A008357 1,60,792,4724,18096,52716,127816,271908,524640,938652,1581432,
%T A008357 2537172,3908624,5818956,8413608,11862148,16360128,22130940,29427672,
%U A008357 38534964,49770864,63488684,80078856
%N A008357 Coordination sequence for D_6 lattice.
%H A008357 T. D. Noe, <a href="/A008357/b008357.txt">Table of n, a(n) for n = 0..1000</a>
%H A008357 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 A008357 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 A008357 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 A008357 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 A008357 M. O'Keeffe, <a href="/A008527/a008527.pdf">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
%H A008357 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A008357 G.f.: (x^6+54*x^5+447*x^4+852*x^3+447*x^2+54*x+1)/(x-1)^6. [_Colin Barker_, Sep 26 2012]
%p A008357 4/15*n*(37+130*n^2+58*n^4);
%Y A008357 A row of array A103903.
%K A008357 nonn,easy
%O A008357 0,2
%A A008357 _N. J. A. Sloane_ and _J. H. Conway_