A047002 T(n,n), array T given by A047000.

1, 1, 2, 7, 23, 83, 299, 1107, 4122, 15523, 58769, 223848, 856085, 3286687, 12656513, 48871469, 189145479, 733547091, 2849962925, 11090427510, 43219527353, 168645172164, 658834266936, 2576566240218, 10086236606187

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Comments

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• C. Banderier, C. Krattenthaler, A. Krinik, D. Kruchinin, V. Kruchinin, D. Nguyen, and M. Wallner, Explicit formulas for enumeration of lattice paths: basketball and the kernel method, arXiv preprint arXiv:1609.06473 [math.CO], 2016.

Crossrefs

Cf. A047000, A278398.

Programs

Mathematica

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];
seq[25] (* Jean-François Alcover, Jul 11 2018, after Andrew Howroyd *)

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