login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A072241
Number of distinct partitions of Fibonacci(n).
2
1, 1, 1, 1, 2, 3, 6, 18, 76, 512, 6378, 173682, 12769602, 3328423936, 4338469000206, 43848229368772905, 5999189517441089061374, 22578203777383772718280932410, 5759108897879943749493986821813718586, 313503492905074747917062873989282073311633745920
OFFSET
0,5
LINKS
FORMULA
a(n) = A000009(A000045(n)).
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jul 06 2002
EXTENSIONS
a(0)=1 prepended and a(19) added by Alois P. Heinz, Apr 06 2021
STATUS
approved