OFFSET
1,2
LINKS
Bruno Berselli, Table of n, a(n) for n = 1..300
Wikipedia, Dirichlet convolution.
FORMULA
a(n) = sum(Fibonacci(d)*Fibonacci(n/d), d|n). [Emanuele Munarini, Feb 14 2014]
G.f.: Sum_{k>=1} Fibonacci(k) * x^k/(1 - x^k - x^(2*k)). - Ilya Gutkovskiy, Jul 24 2019
a(n) ~ 2 * ((1+sqrt(5))/2)^n / sqrt(5). - Vaclav Kotesovec, Sep 11 2019
MATHEMATICA
Table[Sum[Fibonacci[d] Fibonacci[n/d], {d, Divisors[n]}], {n, 1, 100}] (* Emanuele Munarini, Feb 14 2014 *)
PROG
(Maxima) a(n) := lsum(fib(d)*fib(n/d), d, listify(divisors(n)));
makelist(a(n), n, 1, 40); /* Emanuele Munarini, Feb 14 2014 */
(PARI) a(n) = sumdiv(n, d, fibonacci(d)*fibonacci(n/d)); \\ Michel Marcus, Feb 14 2014
(Magma) [&+[Fibonacci(d)*Fibonacci(n div d): d in Divisors(n)]: n in [1..40]]; // Bruno Berselli, Feb 11 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved