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

%I A093997 #17 Dec 02 2020 08:53:14
%S A093997 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 A093997 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 A093997 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 A093997 Number of partitions of n with an odd number of distinct Fibonacci parts.
%H A093997 Alois P. Heinz, <a href="/A093997/b093997.txt">Table of n, a(n) for n = 0..10946</a>
%F A093997 G.f.: (Product_{k>=2} (1 + x^{F_k}) - Product_{k>=2} (1 - x^{F_k}))/2.
%p A093997 F:= combinat[fibonacci]:
%p A093997 b:= proc(n, i, t) option remember; `if`(n=0, t, `if`(i<2, 0,
%p A093997        b(n, i-1, t)+`if`(F(i)>n, 0, b(n-F(i), i-1, 1-t))))
%p A093997     end:
%p A093997 a:= proc(n) local j; for j from ilog[(1+sqrt(5))/2](n+1)
%p A093997        while F(j+1)<=n do od; b(n, j, 0)
%p A093997     end:
%p A093997 seq(a(n), n=0..100);  # _Alois P. Heinz_, Jul 11 2013
%t A093997 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 A093997 Cf. A000119.
%K A093997 nonn,look,easy
%O A093997 0,9
%A A093997 _N. Sato_, May 24 2004
%E A093997 Edited and extended by _Robert G. Wilson v_, May 29 2004