A130716 a(0)=a(1)=a(2)=1, a(n)=0 for n>2.

1, 1, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,1

Comments

With different signs this sequence is the convolutional inverse of the Fibonacci sequence: 1, -1, -1, 0, 0, ... - Tanya Khovanova, Jul 14 2007

Inverse binomial transform of A000124. - R. J. Mathar, Jun 13 2008

Partial sums give A158799. [Jaroslav Krizek, Dec 06 2009]

Links

Table of n, a(n) for n=0..86.

Andrei Asinowski, Cyril Banderier, Valerie Roitner, Generating functions for lattice paths with several forbidden patterns, (2019).

Formula

Given g.f. A(x), then B(a) = A(q) / q satisfies 0 = f(B(q), B(q^2)) where f(u, v) = v - u * (u - 2). - Michael Somos, Oct 22 2013

Euler transform of length 3 sequence [ 1, 0, -1]. - Michael Somos, Oct 22 2013

G.f. is third cyclotomic polynomial.

G.f.: (1 - x^3) / (1 - x).

Convolution inverse is A049347. - Michael Somos, Oct 22 2013

Example

G.f. = 1 + x + x^2.
G.f. = 1/q + 1 + q.

Mathematica

a[ n_] := Boole[ n>=0 && n<=2]; (* Michael Somos, Oct 22 2013 *)

Prog

(PARI) {a(n) = n>=0 && n<=2}; /* Michael Somos, Oct 22 2013 */

Crossrefs

Cf. A049347.

Sequence in context: A266678 A267936 A263013 * A014102 A014195 A014096

Adjacent sequences: A130713 A130714 A130715 * A130717 A130718 A130719

Keyword

easy,nonn

Author

Paul Curtz and Tanya Khovanova, Jul 01 2007

Status

approved