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Coordination sequence for root lattice B_4.
5

%I #19 Sep 06 2023 01:34:42

%S 1,32,224,768,1856,3680,6432,10304,15488,22176,30560,40832,53184,

%T 67808,84896,104640,127232,152864,181728,214016,249920,289632,333344,

%U 381248,433536,490400,552032,618624,690368

%N Coordination sequence for root lattice B_4.

%H Vincenzo Librandi, <a href="/A022146/b022146.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, a(n) = 32*n^3 - 16*n^2 + 16*n. - _Ralf Stephan_, Sep 03 2003

%F G.f.: (1+28*x+102*x^2+60*x^3+x^4)/(1-x)^4 = 1+32*x*(x+1)*(2*x+1)/(1-x)^4. - Colin Barker, Apr 13 2012

%t CoefficientList[Series[(1+28*x+102*x^2+60*x^3+x^4)/(1-x)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Apr 20 2012 *)

%o (Magma) [1] cat[32*n^3 - 16*n^2 + 16*n: 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)