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

0,2

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).

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

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 *)

Crossrefs

Cf. A035749.

Sequence in context: A055754 A297082 A282154 * A035475 A288458 A042110

Adjacent sequences: A035704 A035705 A035706 * A035708 A035709 A035710

Keyword

nonn,easy

Author

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

Extensions

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

Formula clarified by Harvey P. Dale, Jun 21 2011

Status

approved