A148303 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, 1), (-1, 0, 1), (0, 1, -1), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 5, 13, 38, 119, 392, 1322, 4723, 17050, 63318, 241270, 927321, 3646707, 14487316, 58273122, 237345018, 974596819, 4042834966, 16899686492, 71177203798, 301888303055, 1288368101304, 5531248745963, 23874467843991, 103578452298336, 451465919599721, 1976580424093861, 8689421522149543

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A343937 A369729 A149858 * A148304 A149859 A000800

Adjacent sequences: A148300 A148301 A148302 * A148304 A148305 A148306

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved