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A328139 Number of self-avoiding planar walks starting at (0,0), ending at (n,0), not extending above the line (x,2x) or below the line (x,-2x), and using steps (0,1), (-1,1), and (1,-1) with the restriction that (-1,1) and (1,-1) are always immediately followed by (0,1). 2
1, 1, 2, 4, 11, 29, 80, 222, 622, 1758, 5000, 14296, 41049, 118281, 341852, 990570, 2876821, 8371453, 24403371, 71248708, 208311036, 609812089, 1787215592, 5243371099, 15397785369, 45257023128, 133126287754, 391890954915, 1154427358177, 3402881326012 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2100

Alois P. Heinz, Animation of a(7) = 222 walks

Wikipedia, Lattice path

Wikipedia, Self-avoiding walk

MAPLE

b:= proc(x, y, t) option remember; `if`(x<0 or

       abs(y)>2*x, 0, `if`(x=0, 1, b(x-1, y, 1)+

      `if`(t=1, b(x-1, y+1, 0)+b(x+1, y-1, 0), 0)))

    end:

a:= n-> b(n, 0$2):

seq(a(n), n=0..32);

MATHEMATICA

b[x_, y_, t_] := b[x, y, t] = If[x < 0 || Abs[y] > 2 x, 0, If[x==0, 1, b[x - 1, y, 1] + If[t==1, b[x - 1, y + 1, 0] + b[x + 1, y - 1, 0], 0]]];

a[n_] := b[n, 0, 0];

a /@ Range[0, 32] (* Jean-Fran├žois Alcover, May 13 2020, after Maple *)

CROSSREFS

Cf. A328140.

Sequence in context: A118311 A132836 A148140 * A148141 A317879 A148142

Adjacent sequences:  A328136 A328137 A328138 * A328140 A328141 A328142

KEYWORD

nonn,walk

AUTHOR

Alois P. Heinz, Oct 04 2019

STATUS

approved

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Last modified August 14 10:58 EDT 2022. Contains 356116 sequences. (Running on oeis4.)