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

0,6

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A371222 A085794 A336939 * A004548 A125921 A321457

Adjacent sequences: A238999 A239000 A239001 * A239003 A239004 A239005

Keyword

nonn,easy,look

Author

Clark Kimberling, Mar 08 2014

Status

approved