A239000 Number of partitions of n using Fibonacci numbers > 2.

1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 1, 2, 1, 3, 2, 2, 4, 2, 4, 4, 3, 7, 4, 5, 8, 5, 9, 8, 7, 12, 9, 11, 13, 11, 17, 14, 15, 20, 16, 22, 22, 20, 29, 24, 27, 33, 28, 37, 36, 35, 45, 40, 46, 50, 47, 60, 55, 58, 69, 62, 75, 76, 73, 91, 84, 91, 102, 95, 114, 112, 113

Offset: 0

Author

Clark Kimberling, Mar 08 2014

Keywords

• nonn
• easy

Examples

			a(21) counts these partitions: [21], [13,8], [13,5,3], [8,8,5], [8,5,5,3], [5,5,5,3,3], [3,3,3,3,3,3,3].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000045, A003107, A238999.

Programs

Mathematica

p[n_] := IntegerPartitions[n, All, Fibonacci@Range[4, 60]]; Table[p[n], {n, 0, 12}] (*shows partitions*)
a[n_] := Length@p@n; a /@ Range[0, 80] (*counts partitions, A239000*)

PARI

N=66; q='q+O('q^N); Vec( 1/prod(n=1,11,1-q^fibonacci(n+3)) ) \\ Joerg Arndt, Mar 11 2014

Formula

G.f.: 1/Product_{i>=4} (1 - x^Fibonacci(i)).