OFFSET
0,7
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..3000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6).
FORMULA
G.f.: (1 - x)^5/((1 - x)^6 - x^6).
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) for n > 5.
a(n) = (4^n + (1 - t)^n + (1 + t)^n + (3 - t)^n + (3 + t)^n)/(6*2^n) for n > 0 and a(0) = 1, where t = i*sqrt(3) and i = sqrt(-1). - Bruno Berselli, Mar 13 2019
MATHEMATICA
a[n_] := Sum[Binomial[n, 6*k], {k, 0, Floor[n/6]}]; Array[a, 36, 0] (* Amiram Eldar, Jun 21 2021 *)
PROG
(PARI) {a(n) = sum(k=0, n\6, binomial(n, 6*k))}
(PARI) N=66; x='x+O('x^N); Vec((1-x)^5/((1-x)^6-x^6))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Mar 13 2019
STATUS
approved