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Number of ordered ways of writing n as a sum of two Fibonacci numbers (only one 1 is considered as a Fibonacci number).
12

%I #8 Oct 10 2022 12:34:50

%S 0,1,2,3,2,3,2,2,2,3,2,0,2,2,2,3,0,2,0,0,2,2,2,2,0,3,0,0,2,0,0,0,0,2,

%T 2,2,2,0,2,0,0,3,0,0,0,0,2,0,0,0,0,0,0,0,2,2,2,2,0,2,0,0,2,0,0,0,0,3,

%U 0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,0,2,0,0,2,0,0,0,0,2,0,0,0

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

%H Alois P. Heinz, <a href="/A121549/b121549.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A121548(n,2).

%e a(6)=3 because we have 6=1+5=3+3=5+1.

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

%Y Cf. A000045, A121548, A121550, A357688, A357690, A357691.

%K nonn

%O 1,3

%A _Emeric Deutsch_, Aug 07 2006