Search: id:A104545
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%I A104545
%S A104545 1,1,1,3,5,11,25,55,129,303,721,1743,4241,10415,25761,64095,160385,
%T A104545 403263,1018369,2581887,6569089,16767871,42927105,110194175,283574017,
%U A104545 731427583,1890600193,4896499455,12704869633,33021750015,85966113281
%N A104545 Number of Motzkin paths of length n having no consecutive (1,0) steps.
%C A104545 a(n)=A104544(n,0) (n>0).
%F A104545 G.f.=[1-sqrt(1-4z^2*(1+z)^2)]/[2z^2*(1+z)].
%e A104545 a(3)=3 because we have UDH, HUD and UHD, where U=(1,1), D=(1,-1) and 
               H=(1,0) (HHH does not qualify).
%p A104545 G:=(1-sqrt(1-4*z^2*(1+z)^2))/2/z^2/(1+z): Gser:=series(G,z=0,35): 1,seq(coeff(Gser,
               z^n),n=1..31);
%Y A104545 Cf. A001006, A104544.
%Y A104545 Sequence in context: A018116 A167796 A018008 this_sequence A027050 A109249 
               A032364
%Y A104545 Adjacent sequences: A104542 A104543 A104544 this_sequence A104546 A104547 
               A104548
%K A104545 nonn
%O A104545 0,4
%A A104545 Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 14 2005

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