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

0,2

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.

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.

Mathematica

Join[{1}, Table[16n (2-3n+4n^2), {n, 30}]] (* Harvey P. Dale, Oct 21 2011 *)

Prog

(Magma) [1], [16*n*(2-3*n+4*n^2): n in [1..50]]; // Vincenzo Librandi, Oct 22 2011

Crossrefs

Sequence in context: A110275 A348120 A160335 * A339761 A232917 A172201

Adjacent sequences: A019555 A019556 A019557 * A019559 A019560 A019561

Keyword

nonn,easy

Author

mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)

Status

approved