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%I #7 Nov 26 2019 10:54:28
%S 1,2,4,9,18,38,81,171,366,787,1693,3661,7938,17240,37540,81892,178907,
%T 391483,857769,1881618,4132225,9083823,19986954,44014447,97002134,
%U 213933655,472137851,1042626752,2303780392,5093189194,11265742842,24930884645,55196469010,122255756284
%N Number of meanders of length n with Motzkin-steps avoiding the consecutive steps 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.: -(1/2)*(t+1)*((t^3 - t^2 - 2*t + 1)*(t+1) - (1-t)*sqrt((t^3 - t^2 - 2*t + 1)*(t^3 + 3*t^2 + 2*t + 1)))/((t^3 - t^2 - 2*t + 1)*t^2).
%e a(3)=9 as one has 9 meanders of length 3, namely: UUU, UUH, UUD, UDH, UHU, UHD, HUU, HUD and HUH.
%Y Cf. A329666, which counts excursions with same restrictions.
%K nonn,walk
%O 0,2
%A _Valerie Roitner_, Nov 25 2019
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