A035709 Coordination sequence for 14-dimensional cubic lattice.

1, 28, 392, 3668, 25872, 147084, 703640, 2919620, 10746400, 35704060, 108568488, 305568564, 803467056, 1989102444, 4666890936, 10435418532, 22345512000, 46012094940, 91437047240, 175918049300, 328578611536

Offset

0,2

Links

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

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 (14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -1).

Formula

G.f.: ((1+x)/(1-x))^14.

n*a(n) = 28*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Aug 20 2018

Mathematica

CoefficientList[Series[((1+x)/(1-x))^14, {x, 0, 40}], x] (* Harvey P. Dale, Dec 04 2022 *)
(* Alternative: *)
LinearRecurrence[{14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -1}, {1, 28, 392, 3668, 25872, 147084, 703640, 2919620, 10746400, 35704060, 108568488, 305568564, 803467056, 1989102444, 4666890936}, 40] (* Harvey P. Dale, Dec 04 2022 *)

Crossrefs

Sequence in context: A177108 A283637 A126921 * A035476 A042518 A297179

Adjacent sequences: A035706 A035707 A035708 * A035710 A035711 A035712

Keyword

nonn,easy,changed

Author

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

Extensions

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

Status

approved