A035707 Coordination sequence for 12-dimensional cubic lattice.

1, 24, 288, 2312, 14016, 68664, 284000, 1022760, 3281280, 9545560, 25534368, 63521352, 148321344, 327572856, 688686048, 1385794152, 2681291520, 5008112280, 9060853280, 15926230920, 27266245056, 45570869944, 74501171808

Offset: 0

Author

Joan Serra-Sagrista (jserra(AT)ccd.uab.es)

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Muniru A Asiru)
• J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
• Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.
• Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Crossrefs

Cf. A035749.

Programs

Maple

c:=12: seq(coeff(series(((1+x)/(1-x))^c, x,n+1),x,n),n=0..30); # Muniru A Asiru, Jul 01 2018

Mathematica

CoefficientList[Series[((1+x)/(1-x))^12,{x,0,20}],x] (* Harvey P. Dale, Jun 21 2011 *)

Formula

G.f.: ((1+x)/(1-x))^12.

n*a(n) = 24*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Aug 19 2018

Extensions

Recomputed by N. J. A. Sloane, Nov 25 1998

Formula clarified by Harvey P. Dale, Jun 21 2011