login
A306755
a(n) = a(n-6) + a(n-7) with a(0)=7, a(1)=...=a(5)=0, a(6)=6.
2
7, 0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 6, 13, 7, 0, 0, 0, 6, 19, 20, 7, 0, 0, 6, 25, 39, 27, 7, 0, 6, 31, 64, 66, 34, 7, 6, 37, 95, 130, 100, 41, 13, 43, 132, 225, 230, 141, 54, 56, 175, 357, 455, 371, 195, 110, 231, 532, 812, 826, 566, 305, 341, 763, 1344, 1638, 1392, 871, 646, 1104, 2107
OFFSET
0,1
COMMENTS
Conjecture: If p is prime, p divides a(p).
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
Column 6 of A306646.
Sequence in context: A228633 A106226 A229658 * A005070 A135435 A339442
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Mar 08 2019
STATUS
approved