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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A008414.

Programs

Mathematica

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

PARI

a(n) = 2*(4*n^6+70*n^4+196*n^2+45)/45-0^n; \\ Altug Alkan, Dec 18 2017

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

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