%I A121551
%S A121551 1,3,8,19,44,98,213,457,965,2018,4183,8604,17594,35780,72428,146024,
%T A121551 293335,587386,1172836,2335761,4640947,9201531,18208325,35967145,
%U A121551 70929855,139667107,274630886,539309530,1057789244,2072370716
%N 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).
%C A121551 a(n)=Sum(k*A121548(n,k), k=1..n).
%F A121551 g.f.=Sum(z^fibonacci(i), i = 2 .. infinity)/[1-Sum(z^fibonacci(i), i=2.. 
               infinity)]^2.
%e A121551 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.
%p A121551 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);
%Y A121551 Cf. A000045, A121548.
%Y A121551 Sequence in context: A008466 A102712 A054480 this_sequence A077850 A097550 
               A079490
%Y A121551 Adjacent sequences: A121548 A121549 A121550 this_sequence A121552 A121553 
               A121554
%K A121551 nonn
%O A121551 1,2
%A A121551 Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 07 2006