A306757 a(n) = a(n-8) + a(n-9) with a(0)=9, a(1)=...=a(7)=0, a(8)=8.

9, 0, 0, 0, 0, 0, 0, 0, 8, 9, 0, 0, 0, 0, 0, 0, 8, 17, 9, 0, 0, 0, 0, 0, 8, 25, 26, 9, 0, 0, 0, 0, 8, 33, 51, 35, 9, 0, 0, 0, 8, 41, 84, 86, 44, 9, 0, 0, 8, 49, 125, 170, 130, 53, 9, 0, 8, 57, 174, 295, 300, 183, 62, 9, 8, 65, 231, 469, 595, 483, 245, 71, 17, 73, 296, 700

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1,1).

Formula

G.f.: (9 - x^8)/(1 - x^8 - x^9).

a(0) = 9 and a(n) = n*Sum_{k=1..floor(n/8)} binomial(k,n-8*k)/k for n > 0.

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1, 1}, {9, 0, 0, 0, 0, 0, 0, 0, 8}, 100] (* Amiram Eldar, Jun 21 2021 *)

Prog

(PARI) N=99; x='x+O('x^N); Vec((9-x^8)/(1-x^8-x^9))

Crossrefs

Column 8 of A306646.

Sequence in context: A270034 A228635 A229660 * A340982 A334624 A036483

Adjacent sequences: A306754 A306755 A306756 * A306758 A306759 A306760

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 08 2019

Status

approved