A008359 Coordination sequence for D_7 lattice.

1, 84, 1498, 11620, 55650, 195972, 559258, 1371316, 2999682, 6003956, 11193882, 19695172, 33023074, 53163684, 82663002, 124723732, 183309826, 263258772, 370401626, 511690788, 695335522

Offset

0,2

Links

T. D. Noe, 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 [cond-mat.stat-mech], 1997; 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.

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: (x+1)*(x^6 + 76*x^5 + 855*x^4 + 2008*x^3 + 855*x^2 + 76*x + 1)/(1-x)^7. [Colin Barker, Sep 26 2012; corrected by Georg Fischer, May 19 2019]

Maple

484/45*n^6+392/9*n^4+1246/45*n^2+2;

Crossrefs

A row of array A103903.

Sequence in context: A277784 A105942 A219476 * A359934 A166847 A219938

Adjacent sequences: A008356 A008357 A008358 * A008360 A008361 A008362

Keyword

nonn,easy

Author

N. J. A. Sloane and J. H. Conway

Status

approved