A329691 - OEIS

%I #7 Dec 06 2019 11:54:17

%S 1,1,0,1,0,1,1,1,3,2,6,7,11,21,25,52,71,121,204,302,547,828,1417,2333,

%T 3752,6454,10344,17592,29097,48292,81756,134961,228740,381917,642048,

%U 1084489,1817732,3080591,5185373,8772149,14850172,25098840,42612096,72156764,122552908,208140274

%N Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UD, HU, HH and DH.

%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^2+t^3-sqrt(1-2t^2-2t^3+t^4-2t^5+t^6))/(2t^2).

%e a(8)=3 since we have the following 3 excursions of length 8: UUHDDUHD, UHDUUHDD and UUHDUHDD.

%Y Cf. A329692, A329693.

%K nonn,walk

%O 0,9

%A _Valerie Roitner_, Dec 06 2019