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 A329669 #11 Nov 26 2019 10:55:33 %S A329669 1,2,4,10,23,54,129,307,733,1757,4213,10115,24315,58481,140741,338890, %T A329669 816304,1966929,4740758,11428851,27557585,66458601,160295262, %U A329669 386671056,932839439,2250660384,5430575647,13104191607,31622724351,76314992880,184178642468,444513674334,1072865869705 %N A329669 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps HH and DD. %C A329669 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 A329669 G.f.: (1/2)*(-t^3 - 3*t^2 - sqrt(t^6 + 2*t^5 - 3*t^4 - 6*t^3 - 2*t^2 + 1) - 2*t + 1)/((t^3 + 3*t^2 + t - 1)*t). %e A329669 a(2)=4 since we have 4 meanders of length two avoiding HH and DD, namely UU, UH, UD and HU. %Y A329669 See also A329666, which counts excursions with same restrictions. %Y A329669 Cf. A329667, A329665 (meanders avoiding other sets of step sequences of length 2). %K A329669 nonn,walk %O A329669 0,2 %A A329669 _Valerie Roitner_, Nov 25 2019