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

0,3

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.

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 *)

Prog

(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

Crossrefs

Cf. A047000, A278398.

Sequence in context: A119371 A151290 A346627 * A127497 A151291 A150334

Adjacent sequences: A046999 A047000 A047001 * A047003 A047004 A047005

Keyword

nonn

Author

Clark Kimberling

Status

approved