A008416 - OEIS

A008416

Coordination sequence for 8-dimensional cubic lattice.

1, 16, 128, 688, 2816, 9424, 27008, 68464, 157184, 332688, 658048, 1229360, 2187520, 3732560, 6140800, 9785072, 15158272, 22900496, 33830016, 48978352, 69629696, 97364944, 134110592, 182192752, 244396544, 324031120, 425000576

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OFFSET

0,2

COMMENTS

Coordination sequence for 8-dimensional cyclotomic lattice Z[zeta_16].

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)

M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv:math/0508136 [math.CO], 2005-2006.

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

Ross McPhedran, Numerical Investigations of the Keiper-Li Criterion for the Riemann Hypothesis, arXiv:2311.06294 [math.NT], 2023. See p. 6.

Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

FORMULA

G.f.: ((1+x)/(1-x))^8.

a(n) = A008415(n) + A008415(n-1) + a(n-1). - Bruce J. Nicholson, Dec 17 2017

n*a(n) = 16*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Jun 06 2018

MATHEMATICA

CoefficientList[Series[((1 + x)/(1 - x))^8, {x, 0, 26}], x] (* Michael De Vlieger, Dec 18 2017 *)

CROSSREFS

Cf. A008574, A005899, A008412, A008413, A008414, A008415, A008418, A008420.

Cf. A113413, A122542.

Sequence in context: A138331 A290031 A008535 * A045651 A035473 A014972

Adjacent sequences: A008413 A008414 A008415 * A008417 A008418 A008419

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved