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

0,2

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, 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).

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]

Maple

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

Crossrefs

A row of array A103903.

Sequence in context: A168307 A323566 A063011 * A259539 A138898 A229368

Adjacent sequences: A008354 A008355 A008356 * A008358 A008359 A008360

Keyword

nonn,easy

Author

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

Status

approved