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 A329674 #9 Jan 25 2023 12:45:30 %S A329674 1,2,5,13,34,90,240,643,1729,4662,12597,34095,92406,250719,680877, %T A329674 1850457,5032296,13692674,37274438,101509476,276535824,753574253, %U A329674 2054064713,5600176231,15271331416,41651397245,113618996429,309979833301,845805408448,2308108658854,6299205562846 %N A329674 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps DD. %C A329674 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 A329674 G.f.: -(1-3*t-t^2-sqrt(1-2*t-t^2-2*t^3+t^4))/(2*t*(1-2*t-2*t^2)). %F A329674 D-finite with recurrence (n+1)*a(n) +(-4*n-1)*a(n-1) +(n-2)*a(n-2) +(4*n+1)*a(n-3) +(7*n-23)*a(n-4) +2*(n-2)*a(n-5) +2*(-n+5)*a(n-6)=0. - _R. J. Mathar_, Jan 25 2023 %e A329674 a(2)=5 since we have 5 meanders of length 2 avoiding DD, namely UU, UH, UD, HU and HH. %Y A329674 Cf. A004148 (shifted by 1) which counts excursions avoiding consecutive DD steps. %Y A329674 Cf. A329672 and A329673 which count meanders avoiding consecutive UU or HH respectively. %K A329674 nonn,walk %O A329674 0,2 %A A329674 _Valerie Roitner_, Nov 26 2019