A306756 a(n) = a(n-7) + a(n-8) with a(0)=8, a(1)=...=a(6)=0, a(7)=7.

8, 0, 0, 0, 0, 0, 0, 7, 8, 0, 0, 0, 0, 0, 7, 15, 8, 0, 0, 0, 0, 7, 22, 23, 8, 0, 0, 0, 7, 29, 45, 31, 8, 0, 0, 7, 36, 74, 76, 39, 8, 0, 7, 43, 110, 150, 115, 47, 8, 7, 50, 153, 260, 265, 162, 55, 15, 57, 203, 413, 525, 427, 217, 70, 72, 260, 616, 938, 952, 644, 287, 142

Offset: 0

Author

Seiichi Manyama, Mar 08 2019

Keywords

• nonn
• easy

Comments

Conjecture: If p is prime, p divides a(p).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1,1).

Crossrefs

Column 7 of A306646.

Programs

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 1, 1}, {8, 0, 0, 0, 0, 0, 0, 7}, 100] (* Amiram Eldar, Jun 21 2021 *)

PARI

N=66; x='x+O('x^N); Vec((8-x^7)/(1-x^7-x^8))

Formula

G.f.: (8 - x^7)/(1 - x^7 - x^8).

a(0) = 8 and a(n) = n*Sum_{k=1..floor(n/7)} binomial(k,n-7*k)/k for n > 0.