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 A329684 #26 Aug 28 2024 04:18:01
%S A329684 1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A329684 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A329684 1,1,1
%N A329684 Number of excursions of length n with Motzkin-steps forbidding all consecutive steps of length 2 except UD and HH.
%C A329684 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.
%C A329684 This sequence is periodic with a pre-period of length 3 (namely 1, 1, 2) and a period of length 1 (namely 1).
%C A329684 Decimal expansion of 1009/9000. - _Elmo R. Oliveira_, Jun 16 2024
%H A329684 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A329684 G.f.: (1+t^2-t^3)/(1-t).
%F A329684 For n >= 0, a(2) = 2, otherwise a(n) = 1. - _Elmo R. Oliveira_, Jun 16 2024
%e A329684 a(2)=2 since UD and HH are allowed. For n different from 2, only the excursion H^n is allowed.
%t A329684 PadRight[{1, 1, 2}, 100, 1] (* _Paolo Xausa_, Aug 28 2024 *)
%Y A329684 Cf. A329680, A329682, A329683.
%Y A329684 Essentially the same as A294619, A261143 and A141044.
%K A329684 nonn,walk,easy
%O A329684 0,3
%A A329684 _Valerie Roitner_, Nov 29 2019