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%I #11 Nov 26 2019 10:55:33
%S 1,2,4,10,23,54,129,307,733,1757,4213,10115,24315,58481,140741,338890,
%T 816304,1966929,4740758,11428851,27557585,66458601,160295262,
%U 386671056,932839439,2250660384,5430575647,13104191607,31622724351,76314992880,184178642468,444513674334,1072865869705
%N Number of meanders of length n with Motzkin-steps avoiding the consecutive steps HH and DD.
%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^3 - 3*t^2 - sqrt(t^6 + 2*t^5 - 3*t^4 - 6*t^3 - 2*t^2 + 1) - 2*t + 1)/((t^3 + 3*t^2 + t - 1)*t).
%e a(2)=4 since we have 4 meanders of length two avoiding HH and DD, namely UU, UH, UD and HU.
%Y See also A329666, which counts excursions with same restrictions.
%Y Cf. A329667, A329665 (meanders avoiding other sets of step sequences of length 2).
%K nonn,walk
%O 0,2
%A _Valerie Roitner_, Nov 25 2019
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