A288122 Number of partitions of n into prime Fibonacci numbers (A005478).

1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 8, 8, 9, 11, 11, 13, 14, 15, 17, 18, 20, 22, 23, 26, 27, 30, 32, 34, 37, 39, 42, 45, 47, 51, 54, 57, 61, 64, 68, 72, 76, 80, 84, 89, 93, 98, 103, 108, 113, 119, 124, 130, 136, 142, 148, 155, 161, 168, 175, 182, 190, 197, 205, 213, 221, 230

Offset

0,6

Links

Table of n, a(n) for n=0..70.

Eric Weisstein's World of Mathematics, Fibonacci Prime

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=1} 1/(1 - x^A005478(k)).

Example

a(8) = 3 because we have [5, 3], [3, 3, 2] and [2, 2, 2, 2].

Mathematica

CoefficientList[Series[Product[1/(1 - Boole[PrimeQ[Fibonacci[k]]] x^Fibonacci[k]), {k, 1, 30}], {x, 0, 70}], x]

Crossrefs

Cf. A000045, A000607, A003107, A005478, A007000.

Sequence in context: A029099 A029245 A174576 * A060970 A035429 A280169

Adjacent sequences: A288119 A288120 A288121 * A288123 A288124 A288125

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 05 2017

Status

approved