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 A329694 #7 Dec 06 2019 11:54:42 %S A329694 1,1,1,3,3,3,8,12,13,27,50,64,109,215,322,504,966,1616,2526,4578,8115, %T A329694 13143,22836,41162,69410,118536,212498,369226,631631,1119755,1977612, %U A329694 3419130,6014450,10684128,18689970,32807722,58300072,102905556,181031164,321348824,570303658,1007402762 %N A329694 Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, HH and DU. %C A329694 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 at (n,0) and never crossing the x-axis, i.e., staying at nonnegative altitude. %F A329694 G.f.: (1+t)*(1-2t^3-sqrt(1-4t^3-4t^4))/(2t^4). %e A329694 a(4)=3 since we have the following 3 excursions of length 4: UHDH, HUHD and HUDH. %Y A329694 Cf. A248100. %K A329694 nonn,walk %O A329694 0,4 %A A329694 _Valerie Roitner_, Dec 06 2019