A121551 Number of parts in all the compositions of n into Fibonacci numbers (i.e., in all ordered sequences of Fibonacci numbers having sum n; only one 1 is considered as a Fibonacci number).

1, 3, 8, 19, 44, 98, 213, 457, 965, 2018, 4183, 8604, 17594, 35780, 72428, 146024, 293335, 587386, 1172836, 2335761, 4640947, 9201531, 18208325, 35967145, 70929855, 139667107, 274630886, 539309530, 1057789244, 2072370716, 4055782140, 7929563974, 15488792843

Offset

1,2

Comments

a(n) = Sum_{k=1..n} k*A121548(n,k).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..2000

Formula

G.f.: (Sum_{i>=2} z^Fibonacci(i))/(1 - Sum_{i>=2} z^Fibonacci(i))^2.

Example

a(4)=19 because the compositions of 8 into Fibonacci numbers are [1,3],[2,2],[3,1],[1,1,2],[1,2,1],[2,1,1] and [1,1,1,1], having a total of 2+2+2+3+3+3+4 = 19 parts.

Maple

with(combinat): g:=sum(z^fibonacci(i), i=2..20)/(1-sum(z^fibonacci(i), i=2..20))^2: gser:=series(g, z=0, 48): seq(coeff(gser, z, n), n=1..35);

Crossrefs

Cf. A000045, A121548.

Sequence in context: A347310 A332719 A326599 * A189391 A281812 A077850

Adjacent sequences: A121548 A121549 A121550 * A121552 A121553 A121554

Keyword

nonn

Author

Emeric Deutsch, Aug 07 2006

Status

approved