A149725 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, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 75, 287, 1291, 5511, 25329, 111793, 518297, 2346033, 11019069, 50774817, 239978385, 1117987233, 5317529355, 25013236863, 119552222347, 566185604841, 2716303579489, 12937427296805, 62281272464045, 298008646708747, 1438527895424095, 6909251094604987, 33432874382265263, 161099198710910065

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[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 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: A102387 A149723 A149724 * A149726 A149727 A149728

Adjacent sequences: A149722 A149723 A149724 * A149726 A149727 A149728

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved