A093997 Number of partitions of n with an odd number of distinct Fibonacci parts.

0, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 2, 0, 2, 2, 1, 3, 2, 3, 2, 1, 3, 2, 2, 3, 1, 2, 3, 2, 3, 1, 2, 2, 0, 3, 2, 2, 3, 2, 3, 3, 2, 4, 2, 2, 4, 1, 3, 3, 2, 4, 2, 3, 3, 1, 3, 3, 3, 4, 1, 3, 3, 1, 4, 2, 2, 2, 1, 3, 2, 2, 4, 2, 3, 4, 2, 4, 3, 3, 5, 1, 4, 4, 2

Offset: 0

Author

N. Sato, May 24 2004

Keywords

• nonn
• look
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10946

Crossrefs

Cf. A000119.

Programs

Maple

F:= combinat[fibonacci]:
b:= proc(n, i, t) option remember; `if`(n=0, t, `if`(i<2, 0,
       b(n, i-1, t)+`if`(F(i)>n, 0, b(n-F(i), i-1, 1-t))))
    end:
a:= proc(n) local j; for j from ilog[(1+sqrt(5))/2](n+1)
       while F(j+1)<=n do od; b(n, j, 0)
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Jul 11 2013

Mathematica

Take[ CoefficientList[ Expand[ Product[1 + x^Fibonacci[k], {k, 2, 13}]/2 - Product[1 - x^Fibonacci[k], {k, 2, 13}]/2], x], 105] (* Robert G. Wilson v, May 29 2004 *)

Formula

G.f.: (Product_{k>=2} (1 + x^{F_k}) - Product_{k>=2} (1 - x^{F_k}))/2.

Extensions

Edited and extended by Robert G. Wilson v, May 29 2004