A148826 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, -1), (0, -1, 0), (0, 1, 1), (1, 1, -1)}.

1, 1, 3, 8, 27, 85, 309, 1081, 4021, 14818, 57434, 219829, 860342, 3378196, 13535973, 54126261, 218569721, 887699416, 3636969474, 14921133627, 61547442196, 255197583836, 1062706586840, 4434770804244, 18574700299748, 78109639959123, 329306456062837, 1391218406760426, 5894102794883448

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, 1 + 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: A323795 A148824 A148825 * A148827 A148828 A148829

Adjacent sequences: A148823 A148824 A148825 * A148827 A148828 A148829

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved