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 A329673 #9 Jan 25 2023 12:44:06 %S A329673 1,2,4,10,24,60,152,388,1000,2592,6752,17664,46368,122080,322240, %T A329673 852464,2259552,5999552,15954560,42486592,113282048,302386304, %U A329673 807999744,2161077120,5785032448,15498450944,41551965184,111478804480,299274439680,803905119232,2160632498176,5810087371520 %N A329673 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps HH. %C A329673 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 A329673 G.f.: -(1-2*t-2*t^2-sqrt(1-4*t^2-8*t^3-4*t^4))/(2*t*(1-2*t-2*t^2)). %F A329673 D-finite with recurrence (n+1)*a(n) -2*a(n-1) -4*n*a(n-2) +8*(-n+2)*a(n-3) +4*(-n+3)*a(n-4)=0. - _R. J. Mathar_, Jan 25 2023 %e A329673 a(2)=4 since we have 4 meanders of length 2 avoiding HH, namely UU, UH, UD and HU. %Y A329673 Cf. A104545 which counts excursions avoiding consecutive HH steps. Cf. A329672 and A329674 which count meanders avoiding consecutive UU and DD respectively. %K A329673 nonn,walk %O A329673 0,2 %A A329673 _Valerie Roitner_, Nov 26 2019