A104162 - OEIS

A104162

Indicator sequence for the Fibonacci numbers.

1, 2, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

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OFFSET

0,2

COMMENTS

Without multiplicities, this is A010056.

The number of nonnegative integer solutions of x^4 - 10*n^2*x^2 + 25*n^4 - 16 = 0. - Hieronymus Fischer, May 17 2007

LINKS

Table of n, a(n) for n=0..89.

FORMULA

G.f.: Sum_{k>=0} x^Fibonacci(k).

From Hieronymus Fischer, May 17 2007: (Start)

a(n) = 1+floor(arcsinh(sqrt(5)*n/2)/log(phi))-ceiling(arccosh(sqrt(5)*n/2)/log(phi)), for n>0, where phi=(1+sqrt(5))/2.

a(n) = A108852(n) - A108852(n-1) for n>0.

a(n) = A130233(n) - A130233(n-1) for n>0.

a(n) = 1 + A130233(n) - A130234(n) for n>0.

a(n) = A130234(n+1) - A130234(n) for n>=0. (End)

EXAMPLE

a(1)=2 since F(1)=F(2)=1.

PROG

(PARI) a(n)=if(n==1, return(2)); my(k=n^2); k+=((k + 1) << 2); issquare(k) || issquare(k-8) \\ Charles R Greathouse IV, Feb 03 2014; typo corrected by Georg Fischer, Jun 22 2022

CROSSREFS

Cf. A000045.

Partial sums are in A108852.