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%I #7 Dec 03 2019 03:47:38
%S 1,2,3,6,12,24,50,105,221,471,1008,2164,4669,10102,21909,47642,103801,
%T 226549,495284,1084318,2376902,5216543,11460725,25203497,55475172,
%U 122205631,269408827,594343482,1312035579,2898123874,6405224773,14163866716,31336109418,69360335726
%N Number of meanders of length n with Motzkin-steps avoiding the consecutive steps UD and HH.
%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-t^2+t^3-sqrt(t^6+2*t^5-3*t^4-6*t^3-2*t^2+1))/(2*t*(1-2*t-t^2+t^3)).
%e a(3)=6 since we have 6 meanders of length 3, namely UUU, UUH, UHU, UHD, HUU and HUH.
%Y Cf. A329676 which counts excursions avoiding consecutive UD and HH.
%K nonn,walk
%O 0,2
%A _Valerie Roitner_, Nov 29 2019