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A019558 Coordination sequence for F_4 lattice.

%I A019558 #23 Jan 23 2025 16:28:43
%S A019558 1,48,384,1392,3456,6960,12288,19824,29952,43056,59520,79728,104064,
%T A019558 132912,166656,205680,250368,301104,358272,422256,493440,572208,
%U A019558 658944,754032,857856,970800,1093248,1225584
%N A019558 Coordination sequence for F_4 lattice.
%H A019558 Vincenzo Librandi, <a href="/A019558/b019558.txt">Table of n, a(n) for n = 0..10000</a>
%H A019558 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 A019558 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 A019558 a(n) = 16*n*(2 - 3*n + 4*n^2), n >= 1;
%F A019558 G.f.: (1 + 44*x + 198*x^2 + 140*x^3 + x^4)/(1-x)^4 = 1 + 48*x*(x+1)*(3*x+1)/(x-1)^4.
%t A019558 Join[{1},Table[16n (2-3n+4n^2),{n,30}]] (* _Harvey P. Dale_, Oct 21 2011 *)
%o A019558 (Magma) [1] cat [16*n*(2-3*n+4*n^2): n in [1..50]]; // _Vincenzo Librandi_, Oct 22 2011
%K A019558 nonn,easy
%O A019558 0,2
%A A019558 mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)