A151059 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), (0, 0, -1), (0, 1, 0), (1, 0, 0), (1, 1, 0)}.

1, 3, 10, 38, 151, 625, 2675, 11697, 52043, 234891, 1072130, 4939000, 22930993, 107169943, 503692524, 2378872670, 11282929599, 53714328463, 256558536980, 1229004648862, 5902782031035, 28417105740879, 137095496703643, 662675127371465, 3208756135885231, 15561983660317885, 75583524112506556

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A196469 A083692 A308124 * A151060 A151061 A109085

Adjacent sequences: A151056 A151057 A151058 * A151060 A151061 A151062

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved