A034734 Dirichlet convolution of b_n=2^(n-1) with Fibonacci numbers.

1, 3, 6, 13, 21, 48, 77, 163, 298, 593, 1113, 2268, 4329, 8659, 17046, 33949, 67133, 134076, 266325, 531763, 1059702, 2116065, 4222961, 8437812, 16852321, 33680387, 67305930, 134544781, 268949685, 537722088, 1075088093, 2149697251

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Formula

G.f.: Sum_{k>=1} 2^(k-1) * x^k/(1 - x^k - x^(2*k)). - Ilya Gutkovskiy, Jul 24 2019

a(n) ~ 2^(n-1). - Vaclav Kotesovec, Sep 11 2019

Mathematica

Table[Sum[Fibonacci[n/d]*2^(d - 1), {d, Divisors[n]}], {n, 1, 40}] (* Vaclav Kotesovec, Sep 10 2019 *)

Crossrefs

Cf. A000045, A011782.

Sequence in context: A371917 A180750 A047172 * A329766 A019079 A280029

Adjacent sequences: A034731 A034732 A034733 * A034735 A034736 A034737

Keyword

nonn

Author

Erich Friedman

Status

approved