A149259 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, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 4, 11, 40, 118, 456, 1507, 5744, 19426, 75560, 266158, 1030352, 3670444, 14352464, 52199971, 203654240, 745615306, 2926444392, 10849522426, 42528251536, 158358462868, 623214599920, 2340173575694, 9202203205792, 34661061537428, 136684369294096, 517939660469372, 2041346677210144

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A149258 A326423 A366695 * A050911 A149260 A149261

Adjacent sequences: A149256 A149257 A149258 * A149260 A149261 A149262

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved