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

Offset: 0

Author

Paul Barry, Apr 01 2005

Keywords

• easy
• nonn

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

Examples

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

Crossrefs

Cf. A000045.

Partial sums are in A108852.

See also A130233 and A130234.

Programs

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

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)