OFFSET
0,3
COMMENTS
Hankel transform is A166446(n+2). - Paul Barry, Jun 23 2010
LINKS
Andrei Asinowski, Cyril Banderier, Valerie Roitner, Generating functions for lattice paths with several forbidden patterns, (2019).
FORMULA
G.f.: (1-sqrt(1-4x^2))/((1-x)2x^2);
a(n) = Sum_{k=0..floor(n/2)} binomial(2k, k)/(k+1).
Conjecture: -(n+2)*a(n) + (n+2)*a(n-1) + 4*(n-1)*a(n-2) + 4*(1-n)*a(n-3) = 0. - R. J. Mathar, Nov 09 2012
G.f.: 1/x^2 - G(0)/(1-x)/x^2, where G(k)= 1 - x/(1 - x/(1 + x/(1 + x/G(k+1) ))); (continued fraction). - Sergei N. Gladkovskii, Jul 17 2013
MAPLE
a:= n-> add(binomial(2*j, j)/(j+1), j=0..n/2): seq(a(n), n=0..36); # Zerinvary Lajos, Apr 30 2007
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 15 2005
STATUS
approved