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A130716 a(0)=a(1)=a(2)=1, a(n)=0 for n>2. 10
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
easy,nonn
AUTHOR
Paul Curtz and Tanya Khovanova, Jul 01 2007
STATUS
approved

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Last modified June 13 10:24 EDT 2024. Contains 373383 sequences. (Running on oeis4.)