A008379 Crystal ball sequence for D_10 lattice.

1, 181, 6621, 101241, 903881, 5590989, 26515269, 102908209, 341661649, 1001294629, 2650436845, 6447019305, 14603375385, 31126140605, 62948716245, 121608649569, 225663101089, 404083136149, 700922413309, 1181618464729, 1941355693161, 3115998965421, 4896195782501

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
• 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 crystal ball sequences
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Programs

Maple

676/4725*x^10-676/945*x^9+1168/315*x^8-664/63*x^7+1796/75*x^6-1708/45*x^5+41176/945*x^4-6568/189*x^3+29342/1575*x^2-634/105*x+1;

Maxima

A008379(x):=676/4725*x^10-676/945*x^9+1168/315*x^8-664/63*x^7+1796/75*x^6-1708/45*x^5+41176/945*x^4-6568/189*x^3+29342/1575*x^2-634/105*x+1$
makelist(A008379(x),x,1,30); /* Martin Ettl, Oct 26 2012 */

Formula

a(n-1) = 676/4725*n^10-676/945*n^9+1168/315*n^8-664/63*n^7+1796/75*n^6-1708/45*n^5+41176/945*n^4-6568/189*n^3+29342/1575*n^2-634/105*n+1.

G.f.: (x^10+170*x^9+4685*x^8+38200*x^7+124850*x^6+183356*x^5+124850*x^4+38200*x^3+4685*x^2+170*x+1)/(1-x)^11. [Colin Barker, May 28 2012]