OFFSET
0,8
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..3000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,2).
FORMULA
G.f.: (1 - x)^6/((1 - x)^7 - x^7).
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) + 2*a(n-7) for n > 6.
MATHEMATICA
a[n_] := Sum[Binomial[n, 7*k], {k, 0, Floor[n/7]}]; Array[a, 36, 0] (* Amiram Eldar, May 25 2021 *)
PROG
(PARI) {a(n) = sum(k=0, n\7, binomial(n, 7*k))}
(PARI) N=66; x='x+O('x^N); Vec((1-x)^6/((1-x)^7-x^7))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Mar 14 2019
STATUS
approved