This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A329667 #7 Nov 25 2019 08:06:39
%S A329667 1,2,3,6,11,21,42,83,167,341,697,1437,2983,6211,12996,27304,57528,
%T A329667 121601,257759,547652,1166299,2489010,5321780,11398972,24456235,
%U A329667 52549847,113077188,243645011,525630690,1135309380,2454863253,5313639848,11512892983,24967852309
%N A329667 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps UU and HH.
%C A329667 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 A329667 G.f.: (1/2)*(1-t^3-3*t^2-sqrt(t^6+2*t^5-3*t^4-6*t^3-2*t^2+1))*(t+1)/((t^2+2*t-1)*t^2).
%e A329667 a(3)=6 since we have 6 meanders of length 3, namely UHU, UDU, UHD, UDH, HUH and HUD.
%o A329667 (PARI) my(t='t+O('t^40)); Vec((1/2)*(1-t^3-3*t^2-sqrt(t^6+2*t^5-3*t^4-6*t^3-2*t^2+1))*(t+1)/((t^2+2*t-1)*t^2)) \\ _Michel Marcus_, Nov 25 2019
%Y A329667 Cf. A329666 (excursions with same forbidden consecutive steps).
%K A329667 nonn,walk
%O A329667 0,2
%A A329667 _Valerie Roitner_, Nov 25 2019