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A093997 Number of partitions of n with an odd number of distinct Fibonacci parts. 5

%I

%S 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,

%T 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,

%U 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

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

%H Alois P. Heinz, <a href="/A093997/b093997.txt">Table of n, a(n) for n = 0..10946</a>

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

%p F:= combinat[fibonacci]:

%p b:= proc(n, i, t) option remember; `if`(n=0, t, `if`(i<2, 0,

%p b(n, i-1, t)+`if`(F(i)>n, 0, b(n-F(i), i-1, 1-t))))

%p end:

%p a:= proc(n) local j; for j from ilog[(1+sqrt(5))/2](n+1)

%p while F(j+1)<=n do od; b(n, j, 0)

%p end:

%p seq(a(n), n=0..100); # _Alois P. Heinz_, Jul 11 2013

%t 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 *)

%Y Cf. A000119.

%K nonn,look,easy

%O 0,9

%A _N. Sato_, May 24 2004

%E Edited and extended by _Robert G. Wilson v_, May 29 2004

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Last modified September 23 12:11 EDT 2021. Contains 347617 sequences. (Running on oeis4.)