A072241 Number of distinct partitions of Fibonacci(n).

1, 1, 1, 1, 2, 3, 6, 18, 76, 512, 6378, 173682, 12769602, 3328423936, 4338469000206, 43848229368772905, 5999189517441089061374, 22578203777383772718280932410, 5759108897879943749493986821813718586, 313503492905074747917062873989282073311633745920

Offset: 0

Author

Robert G. Wilson v, Jul 06 2002

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..23

Crossrefs

Cf. A000009, A000045, A072214.

Programs

Maple

F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(
     `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
    end:
a:= n-> g(F(n)):
seq(a(n), n=0..18);  # Alois P. Heinz, Apr 06 2021

Mathematica

Table[ PartitionsQ[ Fibonacci[n]], {n, 1, 19}]

Formula

a(n) = A000009(A000045(n)).

Extensions

a(0)=1 prepended and a(19) added by Alois P. Heinz, Apr 06 2021