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%I #7 Dec 06 2019 11:54:42
%S 1,1,1,3,3,3,8,12,13,27,50,64,109,215,322,504,966,1616,2526,4578,8115,
%T 13143,22836,41162,69410,118536,212498,369226,631631,1119755,1977612,
%U 3419130,6014450,10684128,18689970,32807722,58300072,102905556,181031164,321348824,570303658,1007402762
%N Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, HH and DU.
%C The Motzkin step set is U=(1,1), H=(1,0) and D=(1,-1). An excursion is a path starting at (0,0), ending at (n,0) and never crossing the x-axis, i.e., staying at nonnegative altitude.
%F G.f.: (1+t)*(1-2t^3-sqrt(1-4t^3-4t^4))/(2t^4).
%e a(4)=3 since we have the following 3 excursions of length 4: UHDH, HUHD and HUDH.
%Y Cf. A248100.
%K nonn,walk
%O 0,4
%A _Valerie Roitner_, Dec 06 2019
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