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%I #26 Oct 21 2022 21:40:06
%S 1,72,912,5336,20256,58728,142000,301560,581184,1038984,1749456,
%T 2805528,4320608,6430632,9296112,13104184,18070656,24442056,32497680,
%U 42551640,54954912,70097384,88409904,110366328,136485568,167333640,203525712,245728152,294660576
%N Coordination sequence for C_6 lattice.
%H Seiichi Manyama, <a href="/A019562/b019562.txt">Table of n, a(n) for n = 0..10000</a>
%H 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 R. Bacher, P. de la Harpe and B. Venkov, <a href="https://doi.org/10.5802/aif.1689">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 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).
%F G.f.: (1+6*x+x^2)*(1+60*x+134*x^2+60*x^3+x^4)/(1-x)^6.
%F a(n) = A008414(2*n). - _Seiichi Manyama_, Jun 08 2018
%t Join[{1}, LinearRecurrence[{6, -15, 20, -15, 6, -1}, {72, 912, 5336, 20256, 58728, 142000}, 28]] (* _Jean-François Alcover_, Dec 08 2018 *)
%t CoefficientList[Series[(1+66 x+495 x^2+924 x^3+495 x^4+66 x^5+ x^6)/ (-1+x)^6,{x,0,60}],x] (* _Harvey P. Dale_, Jun 06 2021 *)
%Y Cf. A008414.
%K nonn,easy
%O 0,2
%A Michael Baake (mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de)
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