Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #28 Mar 11 2020 22:51:37
%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