# [seqfan] Fibonacci analog of A085755

Richard Mathar mathar at strw.leidenuniv.nl
Wed Mar 24 17:17:04 CET 2010

```The number of partitions of n into a Fibonacci number of Fibonacci parts
seems not to be in the OEIS (?), although it is more obvious to
decompose a number additively into Fibonacci parts than prime parts:

offset 2:
2,3,3,5,5,6,7,9,10,11,12,16,16,20,23,25,27,
31,32,41,43,48,53,60,64,72,79,90,91,104,110,124,135,
146,156,176,184,203,216,239,253,275,294,322,336,372,..

a(2)=2 ways for 2
2, "=", [1, 1]
2, "=", [2]

a(3)=3 ways for 3
3, "=", [1, 1, 1]
3, "=", [1, 2]
3, "=", [3]

a(4)=3 ways for 4
4, "=", [1, 1, 2]
4, "=", [2, 2]
4, "=", [1, 3]

a(5)=5 ways for 5
5, "=", [1, 1, 1, 1, 1]
5, "=", [1, 2, 2]
5, "=", [1, 1, 3]
5, "=", [2, 3]
5, "=", [5]

One could also ask for the number of partitions of n into a prime number
of Fibonacci parts or a Fibonacci number of prime parts...

1,1,1,2,2,3,2,3,4,4,4,6,5,7,8,9,8,...
1,2,3,4,5,7,6,10,10,14,13,19,19,26,26,33,34,...

Richard Mathar

```