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

0,2

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.

See also A130233 and A130234.

Sequence in context: A160381 A089311 A086784 * A145679 A007273 A016319

Adjacent sequences: A104159 A104160 A104161 * A104163 A104164 A104165

Keyword

easy,nonn

Author

Paul Barry, Apr 01 2005

Status

approved