OFFSET
0,9
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..3556
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1,1).
FORMULA
G.f.: (1-x)^6/((1-x)^7-x^8).
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7)+a(n-8) for n > 7.
a(n) = A017857(7*n).
MATHEMATICA
a[n_] := Sum[Binomial[k, 7*(n-k)], {k, 0, n}]; Array[a, 40, 0] (* Amiram Eldar, Jun 21 2021 *)
PROG
(PARI) {a(n) = sum(k=0, n, binomial(k, 7*(n-k)))}
(PARI) N=66; x='x+O('x^N); Vec((1-x)^6/((1-x)^7-x^8))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Mar 06 2019
STATUS
approved