A121550 Number of ordered ways of writing n as a sum of three Fibonacci numbers (only one 1 is considered as a Fibonacci number).

0, 0, 1, 3, 6, 7, 9, 9, 10, 9, 12, 12, 9, 9, 10, 12, 12, 12, 12, 6, 9, 6, 12, 13, 9, 12, 12, 9, 12, 6, 12, 6, 0, 9, 6, 9, 15, 9, 13, 9, 6, 12, 9, 12, 9, 0, 12, 6, 6, 12, 0, 6, 0, 0, 9, 6, 9, 12, 9, 15, 9, 6, 13, 6, 9, 6, 0, 12, 9, 9, 12, 0, 9, 0, 0, 12, 6, 6, 6, 0, 12, 0, 0, 6, 0, 0, 0, 0, 9, 6, 9, 12

Offset

1,4

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

G.f.: (Sum_{i>=2} x^Fibonacci(i))^3.

a(n) = A121548(n,3).

Example

a(6)=7 because we have 6=1+2+3=1+3+2=2+1+3=2+3+1=3+1+2=3+2+1=2+2+2.

Maple

with(combinat): g:=sum(z^fibonacci(i), i=2..30)^3: gser:=series(g, z=0, 130): seq(coeff(gser, z, n), n=1..126);

Crossrefs

Cf. A000045, A121548, A121549, A357688, A357690, A357691.

Sequence in context: A181911 A181919 A021735 * A067751 A283762 A088045

Adjacent sequences: A121547 A121548 A121549 * A121551 A121552 A121553

Keyword

nonn

Author

Emeric Deutsch, Aug 07 2006

Status

approved