A008357 Coordination sequence for D_6 lattice.

1, 60, 792, 4724, 18096, 52716, 127816, 271908, 524640, 938652, 1581432, 2537172, 3908624, 5818956, 8413608, 11862148, 16360128, 22130940, 29427672, 38534964, 49770864, 63488684, 80078856

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, 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).
• M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
• M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

A row of array A103903.

Programs

Maple

4/15*n*(37+130*n^2+58*n^4);

Formula

G.f.: (x^6+54*x^5+447*x^4+852*x^3+447*x^2+54*x+1)/(x-1)^6. [Colin Barker, Sep 26 2012]