A035712 Coordination sequence for 17-dimensional cubic lattice.

1, 34, 578, 6562, 56066, 385186, 2220098, 11058466, 48663554, 192441122, 693230658, 2300164770, 7094825730, 20501991330, 55871829570, 144411206178, 355761664002, 838944980514, 1900906442306, 4152257037218, 8769652761346, 17955289409186, 35721495233602

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Colin Barker)

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 (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).

Formula

G.f.: ((1+x)/(1-x))^17.

a(n) = (2*(638512875 + 4851868680*n^2 + 4215249348*n^4 + 1045091320*n^6 + 99734206*n^8 + 4181320*n^10 + 80444*n^12 + 680*n^14 + 2*n^16)) / 638512875 for n>0. - Colin Barker, Apr 20 2017

n*a(n) = 34*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Aug 20 2018

Prog

(PARI) Vec(((1+x)/(1-x))^17 + O(x^30)) \\ Colin Barker, Apr 20 2017

Crossrefs

Sequence in context: A330412 A089938 A126924 * A302955 A161647 A161991

Adjacent sequences: A035709 A035710 A035711 * A035713 A035714 A035715

Keyword

nonn,easy

Author

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

Extensions

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

Status

approved