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

Author

Ilya Gutkovskiy, Jun 05 2017

Keywords

• nonn

Examples

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

Links

• Eric Weisstein's World of Mathematics, Fibonacci Prime
• Index entries for related partition-counting sequences

Crossrefs

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

Programs

Mathematica

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

Formula

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