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

0,9

Links

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

Formula

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

Example

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].

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*)

Prog

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

Crossrefs

Cf. A000045, A003107, A238999.

Sequence in context: A236480 A236508 A364784 * A105248 A289495 A076302

Adjacent sequences: A238997 A238998 A238999 * A239001 A239002 A239003

Keyword

nonn,easy

Author

Clark Kimberling, Mar 08 2014

Status

approved