A008420 Coordination sequence for 10-dimensional cubic lattice.

1, 20, 200, 1340, 6800, 28004, 97880, 299660, 822560, 2060980, 4780008, 10377180, 21278640, 41517060, 77548920, 139380012, 242080320, 407782740, 668274440, 1068305020, 1669752016, 2556801700, 3842321560, 5675620300

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 (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

Programs

Mathematica

CoefficientList[Series[((1 + x)/(1 - x))^10, {x, 0, 30}], x] (* Wesley Ivan Hurt, Apr 18 2017 *)

Formula

G.f.: ((1+x)/(1-x))^10.

n*a(n) = 20*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Jun 06 2018