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

0,4

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

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

Crossrefs

Cf. A240224, A000119, A000045.

Sequence in context: A029618 A330656 A264399 * A283893 A112427 A098229

Adjacent sequences: A240222 A240223 A240224 * A240226 A240227 A240228

Keyword

nonn,look

Author

Wolfdieter Lang, Apr 07 2014

Extensions

More terms from Alois P. Heinz, Sep 16 2015

Status

approved