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Dirichlet convolution of b_n=2^(n-1) with Fibonacci numbers.
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%I #10 Sep 11 2019 05:12:08

%S 1,3,6,13,21,48,77,163,298,593,1113,2268,4329,8659,17046,33949,67133,

%T 134076,266325,531763,1059702,2116065,4222961,8437812,16852321,

%U 33680387,67305930,134544781,268949685,537722088,1075088093,2149697251

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

%F G.f.: Sum_{k>=1} 2^(k-1) * x^k/(1 - x^k - x^(2*k)). - _Ilya Gutkovskiy_, Jul 24 2019

%F a(n) ~ 2^(n-1). - _Vaclav Kotesovec_, Sep 11 2019

%t Table[Sum[Fibonacci[n/d]*2^(d - 1), {d, Divisors[n]}], {n, 1, 40}] (* _Vaclav Kotesovec_, Sep 10 2019 *)

%Y Cf. A000045, A011782.

%K nonn

%O 1,2

%A _Erich Friedman_