OFFSET
0,1
COMMENTS
Conjecture: If p is prime, p divides a(p).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Johann Cigler, Recurrences for certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials, arXiv:2212.02118 [math.NT], 2022.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1,1).
FORMULA
G.f.: (7 - x^6)/(1 - x^6 - x^7).
a(0) = 7 and a(n) = n*Sum_{k=1..floor(n/6)} binomial(k,n-6*k)/k for n > 0.
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 1, 1}, {7, 0, 0, 0, 0, 0, 6}, 100] (* Amiram Eldar, Jun 21 2021 *)
PROG
(PARI) N=66; x='x+O('x^N); Vec((7-x^6)/(1-x^6-x^7))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Mar 08 2019
STATUS
approved