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A328140 Total number of nodes in all 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, 2, 8, 22, 81, 260, 854, 2738, 8710, 27550, 86696, 271726, 848681, 2642662, 8207726, 25434686, 78663773, 242865100, 748650655, 2304552576, 7085109570, 21757557324, 66745430284, 204559349854, 626379255199, 1916485240548, 5859359429380, 17901726707224 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2093

Alois P. Heinz, Animation of A328139(7) = 222 walks with a(7) = 2738 nodes

Wikipedia, Lattice path

Wikipedia, Self-avoiding walk

MAPLE

b:= proc(x, y, t) option remember; (p-> p+[0, p[1]])(`if`(x<0

       or abs(y)>2*x, 0, `if`(x=0, [1, 0], 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)[2]:

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

MATHEMATICA

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

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

CROSSREFS

Cf. A328139.

Sequence in context: A121135 A183410 A072929 * A053958 A300370 A191643

Adjacent sequences:  A328137 A328138 A328139 * A328141 A328142 A328143

KEYWORD

nonn,walk

AUTHOR

Alois P. Heinz, Oct 04 2019

STATUS

approved

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Last modified August 9 04:23 EDT 2022. Contains 356016 sequences. (Running on oeis4.)