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

0,9

Links

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

Formula

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

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 *)

Crossrefs

Cf. A000119.

Sequence in context: A370077 A370080 A318498 * A157196 A300410 A362845

Adjacent sequences: A093994 A093995 A093996 * A093998 A093999 A094000

Keyword

nonn,look,easy

Author

N. Sato, May 24 2004

Extensions

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

Status

approved