A238999 Number of partitions of n using Fibonacci numbers > 1.

1, 0, 1, 1, 1, 2, 2, 2, 4, 3, 5, 5, 6, 8, 8, 10, 12, 12, 16, 16, 19, 23, 23, 28, 31, 33, 40, 41, 47, 53, 56, 64, 69, 75, 86, 89, 101, 109, 117, 131, 139, 151, 168, 175, 195, 208, 223, 245, 259, 280, 304, 320, 350, 370, 397, 430, 452, 488, 521, 550, 596, 626

Offset

0,6

Links

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

Formula

G.f.: 1/Product_{i>=3} (1 - x^Fibonacci(i)).

Example

a(12) counts these partitions:  822, 552, 5322, 3333, 33222, 222222.

Mathematica

p[n_] := IntegerPartitions[n, All, Fibonacci@Range[3, 60]]; Table[p[n], {n, 0, 12}] (*shows partitions*)
a[n_] := Length@p@n; a /@ Range[0, 80] (*counts partitions, A238999*)

Prog

(PARI) N=66; q='q+O('q^N); Vec( 1/prod(n=1, 11, 1-q^fibonacci(n+2)) ) \\ Joerg Arndt, Mar 11 2014

Crossrefs

Cf. A003107, A000045, A239000.

Sequence in context: A138241 A234615 A029145 * A097986 A368689 A210596

Adjacent sequences: A238996 A238997 A238998 * A239000 A239001 A239002

Keyword

nonn,easy

Author

Clark Kimberling, Mar 08 2014

Status

approved