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 A307557 #27 Nov 29 2024 18:00:16
%S A307557 1,2,4,9,20,47,110,264,634,1541,3754,9204,22622,55817,138026,342203,
%T A307557 849984,2115245,5271970,13158944,32886338,82285031,206101422,
%U A307557 516728937,1296664512,3256472235,8184526438,20584627358,51805243138,130456806425,328703655114
%N A307557 Number of Motzkin meanders of length n with no level steps at odd level.
%C A307557 A Motzkin meander is a lattice path with steps from the set {D=-1, H=0, U=1} that starts at (0,0), and never goes below the x-axis.
%H A307557 Andrei Asinowski, Axel Bacher, Cyril Banderier, Bernhard Gittenberger, <a href="https://lipn.univ-paris13.fr/~banderier/Papers/patterns2019.pdf">Analytic combinatorics of lattice paths with forbidden patterns, the vectorial kernel method, and generating functions for pushdown automata</a>, Algorithmica (2019).
%F A307557 G.f.: ((1+t)/sqrt((t-1)*(4*t^2+t-1)) -1) / (2*t).
%F A307557 D-finite with recurrence (n+1)*a(n) +(-n-2)*a(n-1) +(-5*n+3)*a(n-2) +(n+4)*a(n-3) +2*(2*n-5)*a(n-4)=0. - _R. J. Mathar_, Jan 25 2023
%F A307557 a(n) ~ sqrt(13 + 53/sqrt(17)) * (1 + sqrt(17))^n / (sqrt(Pi*n) * 2^(n + 3/2)). - _Vaclav Kotesovec_, Jun 24 2023
%F A307557 a(n) = (A026569(n) + A026569(n+1))/2. - _Mark van Hoeij_, Nov 29 2024
%e A307557 For n = 3 the a(3) = 9 paths are UUU, UUH, UUD, UDU, UDH, HUU, HUD, HHU, HHH.
%Y A307557 Cf. A307555.
%K A307557 nonn
%O A307557 0,2
%A A307557 _Andrei Asinowski_, Apr 14 2019