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

0,2

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).

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

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 *)

Crossrefs

Sequence in context: A158808 A271899 A128797 * A099196 A041618 A055915

Adjacent sequences: A008415 A008416 A008417 * A008419 A008420 A008421

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved