A148267 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, 0), (-1, 1, 1), (1, 0, -1), (1, 0, 0)}

1, 1, 2, 4, 15, 39, 135, 382, 1543, 4843, 18881, 60918, 256074, 874174, 3590229, 12412052, 53420218, 191510935, 810050590, 2923309230, 12779202552, 47321530017, 204011303079, 758221407024, 3351513850093, 12701475190962, 55496678400253, 210743047646368, 939312182558310, 3622442515633786

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, j, k, -1 + n] + aux[-1 + i, j, 1 + 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, 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: A153942 A055466 A342957 * A148268 A148269 A148270

Adjacent sequences: A148264 A148265 A148266 * A148268 A148269 A148270

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved