0,2

Binomial transform of A097331. Binomial transform is A014318. Partial sums of 1+2x/(1-x+sqrt(1-2x-3x^2)) or (1+x+sqrt(1-2x-3x^2))/(1-x+sqrt(1-2x-3x^2)), which is A001006 with an extra leading 1.

Apparently the Motzkin transform of 1, 2, bar(1, -1, -1, 1), where bar() denotes a periodically continued series, as in A057077. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 11 2008]

Starting with offset 1 = iterates of M * [1,1,0,0,0,...] where M = a tridiagonal matrix with [1,1,1,...] in the main and super diagonals and [0,1,1,1,...] in the subdiagonal. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 08 2009]

Hankel transform is A087960(n)=(-1)^binomial(n+1,2). [From Paul Barry (pbarry(AT)wit.ie), Aug 10 2009]

E. Deutsch and B. E. Sagan, Congruences for Catalan and Motzkin numbers and related sequences, J. Num. Theory 117 (2006), 191-215. [See S_n on page 7.]

a(n)=sum{k=0..n, (-1)^(n+k)binomial(n, k)sum{i=0..k, Catalan(k-i)2^i}}.

G.f.: 1/(1-x-x/(1+x/(1-x+x/(1-x/(1-x-x/(1+x/(1-x+x/(1-x/(1-x-x/(1+... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Aug 10 2009]

Sequence in context: A047121 A096753 A022862 this_sequence A099236 A130581 A051236

Adjacent sequences: A097329 A097330 A097331 this_sequence A097333 A097334 A097335

easy,nonn

Paul Barry (pbarry(AT)wit.ie), Aug 05 2004