%I A126223
%S A126223 0,1,2,7,26,98,372,1419,5434,20878,80444,310726,1202852,4665412,
%T A126223 18126760,70538355,274877370,1072515990,4189573740,16383007410,
%U A126223 64126407180,251226790620,985033185240,3865138313790,15176957307876
%N A126223 Number of level steps in all 2-Motzkin paths (i.e. Motzkin paths with 
               blue and red level steps) of length n, without red level steps on 
               the x-axis.
%C A126223 a(n)=Sum(A126222(n,k),k=0..n).
%F A126223 G.f.=(1-2z)[1-2z-sqrt(1-4*z)]/[2z*sqrt(1-4z)].
%e A126223 a(3)=7 because the 2-Motzkin paths without red level steps on the x-axis 
               are BBB, BUD, UBD, URD and UDB, where U=(1,1), D=(1,-1), B=blue (1,
               0), R=red (1,0); they have a total of 3+1+1+1+1 =7 level steps.
%p A126223 G:=(1-2*z)*(1-2*z-sqrt(1-4*z))/2/z/sqrt(1-4*z): Gser:=series(G,z=0,32): 
               seq(coeff(Gser,z,n),n=0..28);
%Y A126223 Cf. A126222.
%Y A126223 Sequence in context: A055988 A001075 A113436 this_sequence A114121 A049775 
               A101850
%Y A126223 Adjacent sequences: A126220 A126221 A126222 this_sequence A126224 A126225 
               A126226
%K A126223 nonn
%O A126223 0,3
%A A126223 Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 28 2006