A328267 Number of walks on cubic lattice starting at (0,0,0), ending at (0,0,n), remaining in the first (nonnegative) octant and using steps which are permutations of (-2,1,2), (-1,0,2), (-1,1,1), (0,0,1).

1, 1, 3, 9, 45, 243, 1611, 11565, 92169, 782775, 7078995, 67106313, 663693597, 6797495115, 71796341151, 778700005929, 8645902267653, 97997326844499, 1131383216210067, 13278579296016357, 158171247347313933, 1909500035430728655, 23334309656230665411

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..851

Wikipedia, Lattice path

Wikipedia, Self-avoiding walk

Maple

b:= proc(l) option remember; `if`(l[-1]=0, 1, (r-> add(
      add(add(`if`(i+j+k=1, (h-> `if`(h[1]<0, 0, b(h)))(
      sort(l-[i, j, k])), 0), k=r), j=r), i=r))([$-2..2]))
    end:
a:= n-> b([0$2, n]):
seq(a(n), n=0..25);

Mathematica

b[l_] := b[l] = If[Last[l] == 0, 1, Function[r, Sum[If[i + j + k == 1, Function[h, If[h[[1]] < 0, 0, b[h]]][Sort[l - {i, j, k}]], 0], {i, r}, {j, r}, {k, r}]][Range[-2, 2]]];
a[n_] := b[{0, 0, n}];
a /@ Range[0, 25] (* Jean-François Alcover, May 13 2020, after Maple *)

Crossrefs

Cf. A002426, A328268.

Sequence in context: A103620 A138315 A337849 * A038059 A369388 A174318

Adjacent sequences: A328264 A328265 A328266 * A328268 A328269 A328270

Keyword

nonn,walk

Author

Alois P. Heinz, Oct 10 2019

Status

approved