A148249 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, 0, 1), (0, 1, 0), (1, -1, -1), (1, -1, 1)}.

1, 1, 2, 4, 13, 36, 120, 405, 1421, 4942, 18005, 66224, 244983, 920546, 3511295, 13437212, 51845126, 202180183, 792038001, 3115664151, 12346400803, 49158528575, 196269393640, 787327344358, 3172273111184, 12812562941630, 51906057389694, 211049230300642, 860180822317259, 3513322522503773

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[i, -1 + j, k, -1 + n] + aux[1 + 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: A148246 A148247 A148248 * A148250 A148251 A144924

Adjacent sequences: A148246 A148247 A148248 * A148250 A148251 A148252

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved