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 A329668 #7 Nov 26 2019 10:54:28 %S A329668 1,2,4,9,18,38,81,171,366,787,1693,3661,7938,17240,37540,81892,178907, %T A329668 391483,857769,1881618,4132225,9083823,19986954,44014447,97002134, %U A329668 213933655,472137851,1042626752,2303780392,5093189194,11265742842,24930884645,55196469010,122255756284 %N A329668 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps HH and DU. %C A329668 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 A329668 G.f.: -(1/2)*(t+1)*((t^3 - t^2 - 2*t + 1)*(t+1) - (1-t)*sqrt((t^3 - t^2 - 2*t + 1)*(t^3 + 3*t^2 + 2*t + 1)))/((t^3 - t^2 - 2*t + 1)*t^2). %e A329668 a(3)=9 as one has 9 meanders of length 3, namely: UUU, UUH, UUD, UDH, UHU, UHD, HUU, HUD and HUH. %Y A329668 Cf. A329666, which counts excursions with same restrictions. %K A329668 nonn,walk %O A329668 0,2 %A A329668 _Valerie Roitner_, Nov 25 2019