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 A329664 #28 Nov 25 2019 08:04:39 %S A329664 1,1,0,1,2,2,4,8,12,21,40,69,122,227,412,747,1386,2567,4744,8851, %T A329664 16566,31004,58268,109858,207368,392331,744072,1413291,2688822, %U A329664 5124738,9781492,18694896,35780444,68566567,131546440,252661515,485806614,935017790,1801327884,3473467328,6703610548 %N A329664 Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UD, HH and DU. %C A329664 The Motzkin step set is U=(1,1), H=(1,0) and D=(1,-1). An excursion is a path starting at (0,0), ending on the x-axis and never crossing the x-axis, i.e., staying at nonnegative altitude. %F A329664 G.f.: (t+1)*(1 - t - sqrt(4*t^4 - 4*t^3 + t^2 - 2*t + 1))/(2*t^3). %e A329664 a(4)=2 as one has 2 excursions of length 4, namely: HUHD and UHDH. %Y A329664 Cf. A004149 (avoiding UD and DU). %Y A329664 Cf. A329666, A329665. %K A329664 nonn,walk %O A329664 0,5 %A A329664 _Valerie Roitner_, Nov 19 2019