A240225 Total number of parts of the partitions of n into distinct Fibonacci numbers.

0, 1, 1, 3, 2, 3, 5, 2, 6, 5, 5, 9, 3, 6, 9, 5, 12, 7, 9, 12, 3, 10, 9, 9, 17, 7, 12, 16, 7, 18, 12, 12, 18, 4, 10, 14, 9, 21, 12, 17, 22, 7, 21, 16, 16, 27, 9, 18, 23, 12, 27, 15, 18, 22, 4, 15, 14, 14, 27, 12, 21, 27, 12, 32, 22, 22, 34, 9, 21, 27, 16, 36

Offset: 0

Author

Wolfdieter Lang, Apr 07 2014

Keywords

• nonn
• look

Comments

For n=0 the empty partition has no parts.

For these partitions see the array A240224 for which the present sequence is the row length sequence.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..17711

Crossrefs

Cf. A240224, A000119, A000045.

Formula

a(n) is the total number of parts of the A000119(n) partitions of n, each having distinct Fibonacci numbers F(n) = A000045(n), n>=2, as parts.

G.f.: Sum_{k>=2} x^Fibonacci(k)/(1 + x^Fibonacci(k)) * Product_{k>=2} (1 + x^Fibonacci(k)). - Ilya Gutkovskiy, Jan 23 2017

Extensions

More terms from Alois P. Heinz, Sep 16 2015