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 A329684 Number of excursions of length n with Motzkin-steps forbidding all consecutive steps of length 2 except UD and HH. 3

%I

%S 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%U 1,1,1

%N Number of excursions of length n with Motzkin-steps forbidding all consecutive steps of length 2 except UD and HH.

%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 on the x-axis and never crossing the x-axis, i.e., staying at nonnegative altitude.

%C This sequence is periodic with a pre-period of length 3 (namely 1, 1, 2) and a period of length 1 (namely 1).

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F G.f.: (1+t^2-t^3)/(1-t).

%e a(2)=2 since UD and HH are allowed. For n different from 2, only the excursion H^n is allowed.

%Y Cf. A329680, A329682, A329683.

%Y Essentially the same as A294619, A261143 and A141044.

%K nonn,walk,easy

%O 0,3

%A _Valerie Roitner_, Nov 29 2019

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Last modified September 25 11:39 EDT 2021. Contains 347654 sequences. (Running on oeis4.)