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A093997
Number of partitions of n with an odd number of distinct Fibonacci parts.
5
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
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: A370080 A372331 A318498 * A157196 A300410 A362845
KEYWORD
nonn,look,easy
AUTHOR
N. Sato, May 24 2004
EXTENSIONS
Edited and extended by Robert G. Wilson v, May 29 2004
STATUS
approved