cp's OEIS Frontend

A239002 Number of partitions of n into distinct parts all of which are Fibonacci numbers greater than 1.

%I A239002 #14 Mar 15 2014 06:50:06
%S A239002 1,0,1,1,0,2,0,1,2,0,2,1,0,3,0,2,2,0,3,0,1,3,0,3,2,0,4,0,2,3,0,3,1,0,
%T A239002 4,0,3,3,0,5,0,2,4,0,4,2,0,5,0,3,3,0,4,0,1,4,0,4,3,0,6,0,3,5,0,5,2,0,
%U A239002 6,0,4,4,0,6,0,2,5,0,5,3,0,6,0,3,4,0,4
%N A239002 Number of partitions of n into distinct parts all of which are Fibonacci numbers greater than 1.
%C A239002 a(n) > 0 if n+1 is a term of the lower Wythoff sequence, A000201; a(n) = 0 if n+1 is a term of the upper Wythoff sequence, A001950.
%H A239002 Alois P. Heinz, <a href="/A239002/b239002.txt">Table of n, a(n) for n = 0..10946</a>
%F A239002 G.f.: Product_{i>=3} (1+x^Fibonacci(i)). - _Alois P. Heinz_, Mar 15 2014
%p A239002 F:= combinat[fibonacci]:
%p A239002 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<3, 0,
%p A239002        b(n, i-1)+`if`(F(i)>n, 0, b(n-F(i), i-1))))
%p A239002     end:
%p A239002 a:= proc(n) local j; for j from ilog[(1+sqrt(5))/2](n+1)
%p A239002        while F(j+1)<=n do od; b(n, j)
%p A239002     end:
%p A239002 seq(a(n), n=0..100);  # _Alois P. Heinz_, Mar 15 2014
%t A239002 f = Table[Fibonacci[n], {n, 3, 75}];  b[n_] := SeriesCoefficient[Product[1 + x^f[[k]], {k, n}], {x, 0, n}]; u = Table[b[n], {n, 0, 60}]  (* A239002 *)
%t A239002 Flatten[Position[u, 0]]  (* A001950 *)
%Y A239002 Cf. A000201, A001950, A000045, A000119, A239003, A000009.
%K A239002 nonn,easy,look
%O A239002 0,6
%A A239002 _Clark Kimberling_, Mar 08 2014