|
|
A008415
|
|
Coordination sequence for 7-dimensional cubic lattice.
|
|
5
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
|
|
FORMULA
|
G.f.: ((1+x)/(1-x))^7.
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)
(PARI) a(n) = 2*(4*n^6+70*n^4+196*n^2+45)/45-0^n; \\ Altug Alkan, Dec 18 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|