A148717 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, 1), (1, -1, -1), (1, 0, -1), (1, 1, 0)}.

1, 1, 3, 7, 24, 71, 266, 881, 3469, 12332, 50040, 186794, 773667, 2991999, 12582929, 49973205, 212688321, 862323174, 3705563783, 15273748851, 66155435101, 276381653991, 1205044479945, 5091121948506, 22322747011858, 95206082315274, 419467191167207, 1803527626027861, 7979621517946516

Offset

0,3

Links

Table of n, a(n) for n=0..28.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A148714 A148715 A148716 * A148718 A003449 A258308

Adjacent sequences: A148714 A148715 A148716 * A148718 A148719 A148720

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved