A148252 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, 1, 0), (1, -1, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 13, 36, 128, 422, 1639, 5949, 24113, 93309, 391828, 1583365, 6804543, 28395349, 124390258, 531687409, 2362484441, 10291265724, 46279573814, 204646979728, 929108004632, 4159489988998, 19039705452731, 86108778313062, 396846467067471, 1810271300484767, 8392688367577943

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[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148250 A148251 A144924 * A268698 A174604 A148253

Adjacent sequences: A148249 A148250 A148251 * A148253 A148254 A148255

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved