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%I #21 Sep 06 2023 01:35:10
%S 1,50,530,2562,8130,20082,42130,78850,135682,218930,335762,494210,
%T 703170,972402,1312530,1735042,2252290,2877490,3624722,4508930,
%U 5545922,6752370,8145810,9744642,11568130,13636402
%N Coordination sequence for root lattice B_5.
%H Vincenzo Librandi, <a href="/A022147/b022147.txt">Table of n, a(n) for n = 0..1000</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="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.
%F a(0) = 1; for n>0, a(n) = (108*n^4 - 88*n^3 + 156*n^2 - 32*n + 6)/3 . - _Philippe Deléham_, Feb 20 2004
%F G.f.: (1+45*x+290*x^2+402*x^3+125*x^4+x^5)/(1-x)^5 = 1+2*x*(25+140*x+206*x^2+60*x^3+x^4)/(1-x)^5. - _Colin Barker_, Apr 13 2012
%t CoefficientList[Series[(1+45*x+290*x^2+402*x^3+125*x^4+ x^5)/(1-x)^5,{x,0,40}],x] (* _Vincenzo Librandi_, Apr 20 2012 *)
%o (Magma) [1] cat[(108*n^4 - 88*n^3 + 156*n^2 - 32*n + 6)/3 : n in [1..40]]; // _Vincenzo Librandi_, Apr 20 2012
%K nonn,easy
%O 0,2
%A mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)
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