cp's OEIS Frontend

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).

%I A121551 #11 Feb 05 2021 07:01:42
%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 70929855,139667107,274630886,539309530,1057789244,2072370716,4055782140,7929563974,15488792843
%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=1..n} k*A121548(n,k).
%H A121551 Alois P. Heinz, <a href="/A121551/b121551.txt">Table of n, a(n) for n = 1..2000</a>
%F A121551 G.f.: (Sum_{i>=2} z^Fibonacci(i))/(1 - Sum_{i>=2} z^Fibonacci(i))^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.
%K A121551 nonn
%O A121551 1,2
%A A121551 _Emeric Deutsch_, Aug 07 2006