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%I #8 Apr 07 2021 11:55:42
%S 1,1,1,1,2,3,6,18,76,512,6378,173682,12769602,3328423936,
%T 4338469000206,43848229368772905,5999189517441089061374,
%U 22578203777383772718280932410,5759108897879943749493986821813718586,313503492905074747917062873989282073311633745920
%N Number of distinct partitions of Fibonacci(n).
%H Alois P. Heinz, <a href="/A072241/b072241.txt">Table of n, a(n) for n = 0..23</a>
%F a(n) = A000009(A000045(n)).
%p F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
%p g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(
%p `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
%p end:
%p a:= n-> g(F(n)):
%p seq(a(n), n=0..18); # _Alois P. Heinz_, Apr 06 2021
%t Table[ PartitionsQ[ Fibonacci[n]], {n, 1, 19}]
%Y Cf. A000009, A000045, A072214.
%K nonn
%O 0,5
%A _Robert G. Wilson v_, Jul 06 2002
%E a(0)=1 prepended and a(19) added by _Alois P. Heinz_, Apr 06 2021