A035711 Coordination sequence for 16-dimensional cubic lattice.

1, 32, 512, 5472, 44032, 285088, 1549824, 7288544, 30316544, 113461024, 387328512, 1219605600, 3575055360, 9832110240, 25537728000, 63001648608, 148348809216, 334834507296, 727126954496, 1524223640416, 3093172083712

Offset

0,2

Comments

Coordination sequence for 16-dimensional cyclotomic lattice Z[zeta_32].

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv math.CO/0508136

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 (16, -120, 560, -1820, 4368, -8008, 11440, -12870, 11440, -8008, 4368, -1820, 560, -120, 16, -1).

Formula

G.f.: ((1+x)/(1-x))^16.

n*a(n) = 32*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Aug 20 2018

Mathematica

CoefficientList[Series[((1+x)/(1-x))^16, {x, 0, 20}], x] (* Harvey P. Dale, Dec 27 2015 *)

Crossrefs

Sequence in context: A371453 A271577 A116003 * A035477 A109384 A248070

Adjacent sequences: A035708 A035709 A035710 * A035712 A035713 A035714

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, Dec 27 2015

Status

approved