A150253 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), (0, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 22, 85, 346, 1440, 6159, 26815, 118327, 528550, 2380917, 10818029, 49483614, 227664763, 1052925406, 4891242953, 22815517629, 106805211439, 501601354770, 2362655629199, 11158244202186, 52826920940209, 250658260040043, 1191794900606386, 5677357811915794, 27092895648509881, 129501831523068156

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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[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: A150250 A150251 A150252 * A150254 A148497 A206736

Adjacent sequences: A150250 A150251 A150252 * A150254 A150255 A150256

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved