A019558 Coordination sequence for F_4 lattice.
1, 48, 384, 1392, 3456, 6960, 12288, 19824, 29952, 43056, 59520, 79728, 104064, 132912, 166656, 205680, 250368, 301104, 358272, 422256, 493440, 572208, 658944, 754032, 857856, 970800, 1093248, 1225584
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, arXiv:cond-mat/9706122, Zeit. f. Kristallographie, 212 (1997), 253-256.
- R. Bacher, P. de la Harpe and B. Venkov, Séries de croissance et séries d'Ehrhart associées aux réseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
Programs
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Magma
[1] cat [16*n*(2-3*n+4*n^2): n in [1..50]]; // Vincenzo Librandi, Oct 22 2011
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Mathematica
Join[{1},Table[16n (2-3n+4n^2),{n,30}]] (* Harvey P. Dale, Oct 21 2011 *)
Formula
a(n) = 16*n*(2 - 3*n + 4*n^2), n >= 1;
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.