0,3

a(n+1)= Y_{n}(n+1)= Z_{n}, n >= 0, in the Derrida et al. 1992 reference (see A064094) for alpha=2, beta =1 (or alpha=1, beta=2).

a(n) = number of Dyck n-paths (A000108) in which each upstep (U) not at ground level is colored red (R) or blue (B). For example, a(3)=3 counts URDD, UBDD, UDUD (D=downstep). - David Callan (callan(AT)stat.wisc.edu), Mar 30 2007

The Hankel transform of this sequence is A002416 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2007

The sequence a(n)/2^n, with g.f. 1/(1-xc(x)/2), has Hankel transform 1/2^n. - Paul Barry (pbarry(AT)wit.ie), Apr 14 2008

N. Bonichon, C. Gavoille And N. Hanusse. Canonical Decomposition of Outerplanar Maps and Application to Enumeration, Coding and Generation. In Proceedings of WG'03, volume 2880 of LNCS, pp. 81-92, 2003.

Alexander Burstein, Sergi Elizalde and Toufik Mansour, Restricted Dumont permutations, Dyck paths and noncrossing partitions, arXiv math.CO/0610234.

G.f.: (1+2*x*c(2*x))/(1+x) = 1/(1-x*c(2*x)) with c(x) g.f. of Catalan numbers A000108.

a(n)= A062992(n-1) = sum((n-m)*binomial(n-1+m, m)*(2^m)/n, m=0..n-1), n >= 1, a(0) := 1.

a(n) = Sum{ k= 0...n, A059365(n, k)*2^(n-k) }. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 19 2004

G.f.: 1/(1-x/(1-2x/(1-2x/(1-2x/(1-.... =1/(1-x-2x^2/(1-4x-4x^2/(1-4x-4x^2/(1-.... (continued fractions). [From Paul Barry (pbarry(AT)wit.ie), Jan 30 2009]

a[0]=1; a[1]=1; a[n_]/; n>=2 := a[n] = a[n-1] + Sum[(a[k] + a[k-1])a[n-k], {k, n-1}]; Table[a[n], {n, 0, 10}] [From David Callan (callan(AT)stat.wisc.edu), Aug 27 2009]

(PARI) a(n)=polcoeff((3-sqrt(1-8*x+x*O(x^n)))/(2+2*x), n)

Adjacent sequences: A064059 A064060 A064061 this_sequence A064063 A064064 A064065

Sequence in context: A136784 A027277 A062992 this_sequence A114191 A107592 A028418

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 13 2001