A022146 Coordination sequence for root lattice B_4.

1, 32, 224, 768, 1856, 3680, 6432, 10304, 15488, 22176, 30560, 40832, 53184, 67808, 84896, 104640, 127232, 152864, 181728, 214016, 249920, 289632, 333344, 381248, 433536, 490400, 552032, 618624, 690368

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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(0) = 1, a(n) = 32*n^3 - 16*n^2 + 16*n. - Ralf Stephan, Sep 03 2003

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

Mathematica

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 *)

Prog

(Magma) [1] cat[32*n^3 - 16*n^2 + 16*n: n in [1..40]]; // Vincenzo Librandi, Apr 20 2012

Crossrefs

Sequence in context: A146089 A250232 A070053 * A160061 A269585 A199913

Adjacent sequences: A022143 A022144 A022145 * A022147 A022148 A022149

Keyword

nonn,easy

Author

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

Status

approved