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A019558 Coordination sequence for F_4 lattice. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
KEYWORD
nonn,easy
AUTHOR
mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)
STATUS
approved

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Last modified May 26 21:01 EDT 2024. Contains 372844 sequences. (Running on oeis4.)