A148235 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, 1, 1), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 4, 13, 35, 118, 341, 1222, 3871, 14095, 46182, 172636, 588711, 2213167, 7681235, 29298637, 104046951, 397960363, 1428060581, 5509869249, 20062858933, 77534482146, 284269944662, 1104891547397, 4091541637473, 15918933390799, 59235013814143, 231394948623317, 867248153419761, 3390021144010261

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[1 + i, -1 + 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: A192443 A189590 A189597 * A151522 A148236 A148237

Adjacent sequences: A148232 A148233 A148234 * A148236 A148237 A148238

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved