A151136 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), (0, 0, -1), (0, 1, 0), (1, 0, 1), (1, 1, 0)}

1, 3, 11, 46, 202, 914, 4230, 19872, 94399, 452259, 2181014, 10573296, 51475524, 251476927, 1232106449, 6051282793, 29780747282, 146818968545, 724903922819, 3583792136390, 17737638719108, 87877559572470, 435750001845817, 2162368515200979, 10737843495197540, 53353981611399815, 265247173093336247

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[i, -1 + j, k, -1 + n] + aux[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: A151134 A151135 A307816 * A151137 A151138 A151139

Adjacent sequences: A151133 A151134 A151135 * A151137 A151138 A151139

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved