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

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, 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, 6, 0, 4, 4, 0, 6, 0, 2, 5, 0, 5, 3, 0, 6, 0, 3, 4, 0, 4

Offset: 0

Author

Clark Kimberling, Mar 08 2014

Keywords

• nonn
• easy
• look

Comments

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.

Links

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

Crossrefs

Cf. A000201, A001950, A000045, A000119, A239003, A000009.

Programs

Maple

F:= combinat[fibonacci]:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<3, 0,
       b(n, i-1)+`if`(F(i)>n, 0, b(n-F(i), i-1))))
    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)
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Mar 15 2014

Mathematica

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 *)
Flatten[Position[u, 0]]  (* A001950 *)

Formula

G.f.: Product_{i>=3} (1+x^Fibonacci(i)). - Alois P. Heinz, Mar 15 2014