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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

A row of array A103903.

Programs

Maple

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

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]