%I A035011
%S A035011 0,1,5,21,89,393,1805,8557,41585,206097,1037717,5293445,
%T A035011 27297737,142078745,745387037,3937603037,20927156705,111818026017,
%U A035011 600318853925,3236724317173
%N A035011 A006318(n) - 1.
%C A035011 Number of occurrences of UD, UHD, UHHD, UHHHD, ... starting at level 
               zero in all Schroeder paths of semilength n (i.e. lattice paths from 
               (0,0) to (2n,0), with steps H=(2,0), U=(1,1) and D=(1,-1) and not 
               going below the x-axis). Example: a(2) = 5 because in the six paths 
               of semilength 2, namely HH, H(UD), (UD)H, (UHD), (UD)(UD), UUDD, 
               we have 5 required occurrences (shown between parentheses). - Emeric 
               Deutsch (deutsch(AT)duke.poly.edu), Dec 28 2003
%F A035011 G.f.=(1-4z+z^2)/[2z(1-z)]-sqrt(1-6z+z^2)/(2z). - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Dec 28 2003
%Y A035011 Cf. A006318.
%Y A035011 Sequence in context: A010917 A015448 A099843 this_sequence A113987 A164037 
               A125784
%Y A035011 Adjacent sequences: A035008 A035009 A035010 this_sequence A035012 A035013 
               A035014
%K A035011 nonn
%O A035011 0,3
%A A035011 N. J. A. Sloane (njas(AT)research.att.com).