A008418 Coordination sequence for 9-dimensional cubic lattice.

1, 18, 162, 978, 4482, 16722, 53154, 148626, 374274, 864146, 1854882, 3742290, 7159170, 13079250, 22952610, 38878482, 63821826, 101880594, 158611106, 241419474, 360027522, 527022162, 758497698, 1074801042, 1501390338

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)
• 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 linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Programs

Mathematica

CoefficientList[Series[((1 + x)/(1 - x))^9, {x, 0, 30}], x] (* Wesley Ivan Hurt, Feb 04 2017 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,18,162,978,4482,16722,53154,148626,374274,864146},30] (* Harvey P. Dale, Aug 01 2024 *)

Formula

G.f.: ((1+x)/(1-x))^9.

n*a(n) = 18*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Jun 06 2018