A148050 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), (0, 1, 1), (1, -1, -1)}.

1, 1, 2, 3, 10, 20, 58, 139, 458, 1160, 3818, 10392, 34670, 97442, 333818, 969459, 3328978, 9938088, 34450338, 104523080, 366290046, 1131762090, 3975840690, 12469787368, 44066215102, 139601191058, 496316131002, 1590475923282, 5665647301990, 18329790880270, 65557254590130, 213555494493479, 766770413340810

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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[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: A148047 A148048 A148049 * A148051 A148052 A148053

Adjacent sequences: A148047 A148048 A148049 * A148051 A148052 A148053

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved