0,2

Table of n, a(n) for n=0..104.

a(n)=max(k | Fib(k)^2<=n)=A130233(floor(sqrt(n)))=floor(arcsinh(sqrt(5n)/2)/log(phi)) where phi=(1+sqrt(5))/2.

G.f.: g(x)=1/(1-x)*sum{k>=1, x^(Fib(k)^2)}.

a(10)=4 since Fib(4)^2=9<=10 but Fib(5)^2=25>10.

Partial sums: A130240. Other related sequences: A000045, A130233, A130234, A130235, A130236, A130237, A130238, A130240, A130243, A130246, A130248, A130239, A130251, A130253, A130257, A130261.

Sequence in context: A318781 A316844 A331245 * A091092 A218461 A186189

Adjacent sequences: A130236 A130237 A130238 * A130240 A130241 A130242

nonn

Hieronymus Fischer, May 17 2007, May 28 2007

approved