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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

A row of array A103903.

Programs

Magma

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

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]