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%I #21 Nov 25 2019 08:03:14
%S 1,2,3,6,11,20,38,72,136,260,499,958,1847,3572,6917,13422,26097,50808,
%T 99049,193354,377857,739148,1447292,2836316,5562774,10918180,21444029,
%U 42143986,82874681,163060540,320996342,632211192,1245727488,2455674532,4842782497,9554018554,18855375593,37224944572
%N Number of meanders of length n with Motzkin-steps avoiding the consecutive steps UD, HH and DU.
%C The Motzkin step set is U=(1,1), H=(1,0) and D=(1,-1). A meander is a path starting at (0,0) and never crossing the x-axis, i.e., staying at nonnegative altitude.
%F G.f.: ((-t-1)*sqrt(4*t^4-4*t^3+t^2-2*t+1)-2*t^3-3*t^2+1)/(4*t^3-2*t^2).
%e a(3)=6 as one has 6 meanders of length 3, namely: UUU, UUH, UHU, UHD, HUU, HUH.
%Y Cf. A308435 (avoiding UD and DU), A329666 (avoiding UU and HH).
%Y Cf. A329664.
%K nonn,walk
%O 0,2
%A _Valerie Roitner_, Nov 19 2019