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%I #23 Jan 14 2024 00:14:56
%S 1,1,2,7,23,83,299,1107,4122,15523,58769,223848,856085,3286687,
%T 12656513,48871469,189145479,733547091,2849962925,11090427510,
%U 43219527353,168645172164,658834266936,2576566240218,10086236606187
%N T(n,n), array T given by A047000.
%C Alternatively, this sequence counts the meanders (walks starting at the origin and ending at any altitude >= 0 that may touch but never go below the x-axis) with n steps from {-2,-1,1,2}. - _David Nguyen_, Dec 20 2016
%H Andrew Howroyd, <a href="/A047002/b047002.txt">Table of n, a(n) for n = 0..200</a>
%H C. Banderier, C. Krattenthaler, A. Krinik, D. Kruchinin, V. Kruchinin, D. Nguyen, and M. Wallner, <a href="https://arxiv.org/abs/1609.06473">Explicit formulas for enumeration of lattice paths: basketball and the kernel method</a>, arXiv preprint arXiv:1609.06473 [math.CO], 2016.
%t seq[n_] := Module[{v = Table[1, n], m = Sum[ x^i, {i, -2, 2}] - 1, p = 1}, For[i = 3, i <= n, i++, p = Expand[p*m]; p = p - Select[p, Exponent[#, x] < 0&]; v[[i]] = ReplaceAll[p, x -> 1]]; v];
%t seq[25] (* _Jean-François Alcover_, Jul 11 2018, after _Andrew Howroyd_ *)
%o (PARI) seq(n)={my(v=vector(n), m=sum(i=-2, 2, x^i)-1, p=1); v[1]=v[2]=1; for(i=3, n, p*=m; p-=frac(p); v[i]=subst(p,x,1)); v} \\ _Andrew Howroyd_, Jun 27 2018
%Y Cf. A047000, A278398.
%K nonn
%O 0,3
%A _Clark Kimberling_
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