A149766 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, 0, 0), (-1, 0, 1), (0, -1, 1), (0, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 73, 311, 1311, 5649, 24813, 109253, 486623, 2180255, 9810137, 44389337, 201532081, 918049895, 4195559999, 19220439983, 88266951791, 406225389833, 1873032183291, 8651794361859, 40027647209457, 185460795520767, 860488331810451, 3997459914921589, 18592433852321707, 86570131609594613

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A149764 A149765 A124464 * A254686 A295374 A212403

Adjacent sequences: A149763 A149764 A149765 * A149767 A149768 A149769

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved