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 A329683 #21 Jun 20 2024 17:46:27 %S A329683 1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, %T A329683 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, %U A329683 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2 %N A329683 Number of excursions of length n with Motzkin-steps forbidding all consecutive steps of length 2 except UH, HH and HD. %C A329683 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 A329683 This sequence is periodic with a pre-period of length 3 (namely 1, 1, 1) and a period of length 1 (namely 2). %C A329683 Decimal expansion of 1001/9000. - _Elmo R. Oliveira_, Jun 16 2024 %H A329683 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1). %F A329683 G.f.: (1 + t^3)/(1 - t). %F A329683 a(n) = 2 for n >= 3. - _Elmo R. Oliveira_, Jun 16 2024 %e A329683 For n >= 3 we always have two allowed excursions, namely UH^(n-2)D and H^n. %e A329683 For n = 0, 1, 2 we have one meander each, namely the empty walk, H and HH. %Y A329683 Cf. A329680, A329682, A329684. %K A329683 nonn,walk,easy %O A329683 0,4 %A A329683 _Valerie Roitner_, Nov 29 2019