A008415 Coordination sequence for 7-dimensional cubic lattice.

1, 14, 98, 462, 1666, 4942, 12642, 28814, 59906, 115598, 209762, 361550, 596610, 948430, 1459810, 2184462, 3188738, 4553486, 6376034, 8772302, 11879042, 15856206, 20889442, 27192718, 35011074, 44623502, 56345954, 70534478

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).

Milan Janjić, On Restricted Ternary Words and Insets, arXiv:1905.04465 [math.CO], 2019.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: ((1+x)/(1-x))^7.

a(n) = 4*n*n*(2*n*n + 7)*(n*n + 14)/45 + 2 - 0^n. - George F. Johnson, Feb 21 2013

a(n) = A008414(n) + A008414(n-1) + a(n-1). - Bruce J. Nicholson, Dec 17 2017

n*a(n) = 14*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Jun 06 2018

Mathematica

CoefficientList[Series[((1+x)/(1-x))^7, {x, 0, 30}], x] (* Harvey P. Dale, Oct 11 2015 *)

Prog

(Python)
R = []
for n in range(29):
    r=4*n*n*(2*n*n +7)*(n*n +14)//45 +2-0**n
    R.append(r)
print(R)
# George F. Johnson Feb 02 2013
(PARI) a(n) = 2*(4*n^6+70*n^4+196*n^2+45)/45-0^n; \\ Altug Alkan, Dec 18 2017

Crossrefs

Cf. A008414.

Sequence in context: A372661 A296987 A008534 * A003206 A206257 A101376

Adjacent sequences: A008412 A008413 A008414 * A008416 A008417 A008418

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved