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A130716 a(0)=a(1)=a(2)=1, a(n)=0 for n>2. 7

%I

%S 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,

%T 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,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

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

%C With different signs this sequence is the convolutional inverse of the Fibonacci sequence: 1, -1, -1, 0, 0, ... - _Tanya Khovanova_, Jul 14 2007

%C Inverse binomial transform of A000124. - _R. J. Mathar_, Jun 13 2008

%C Partial sums give A158799. [_Jaroslav Krizek_, Dec 06 2009]

%H Andrei Asinowski, Cyril Banderier, Valerie Roitner, <a href="https://lipn.univ-paris13.fr/~banderier/Papers/several_patterns.pdf">Generating functions for lattice paths with several forbidden patterns</a>, (2019).

%F 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

%F Euler transform of length 3 sequence [ 1, 0, -1]. - _Michael Somos_, Oct 22 2013

%F G.f. is third cyclotomic polynomial.

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

%F Convolution inverse is A049347. - _Michael Somos_, Oct 22 2013

%e G.f. = 1 + x + x^2.

%e G.f. = 1/q + 1 + q.

%t a[ n_] := Boole[ n>=0 && n<=2]; (* _Michael Somos_, Oct 22 2013 *)

%o (PARI) {a(n) = n>=0 && n<=2}; /* _Michael Somos_, Oct 22 2013 */

%Y Cf. A049347.

%K easy,nonn

%O 0,1

%A _Paul Curtz_ and _Tanya Khovanova_, Jul 01 2007

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Last modified August 6 19:52 EDT 2020. Contains 336256 sequences. (Running on oeis4.)