

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



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
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OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..30.


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)/(1sum(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: A102712 A054480 A191787 * A189391 A281812 A077850
Adjacent sequences: A121548 A121549 A121550 * A121552 A121553 A121554


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Aug 07 2006


STATUS

approved



