A008355 Coordination sequence for D_5 lattice.

1, 40, 370, 1640, 4930, 11752, 24050, 44200, 75010, 119720, 182002, 265960, 376130, 517480, 695410, 915752, 1184770, 1509160, 1896050, 2353000, 2888002, 3509480, 4226290, 5047720, 5983490, 7043752

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.

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 (5, -10, 10, -5, 1).

Formula

a(n) = 2*(9*n^2+1)*(n^2+1) (see MAPLE line).

G.f.: (1+x)*(1+34*x+146*x^2+34*x^3+x^4)/(1-x)^5. [Colin Barker, Apr 14 2012]

Maple

2*(9*n^2+1)*(n^2+1);

Mathematica

CoefficientList[Series[(1+x)*(1+34*x+146*x^2+34*x^3+x^4)/(1-x)^5, {x, 0, 30}], x] (* Vincenzo Librandi, Apr 16 2012 *)

Prog

(Magma) [1]cat[2*(9*n^2+1)*(n^2+1): n in [1..30]]; // Vincenzo Librandi, Apr 16 2012

Crossrefs

A row of array A103903.

Sequence in context: A190312 A229532 A252180 * A229716 A221820 A301528

Adjacent sequences: A008352 A008353 A008354 * A008356 A008357 A008358

Keyword

nonn,easy

Author

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

Status

approved