A151164 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), (0, 0, -1), (0, 0, 1), (0, 1, 1), (1, 0, 1)}.

1, 3, 12, 47, 204, 888, 3998, 18115, 83266, 385720, 1799850, 8449820, 39852336, 188798366, 897534884, 4280688461, 20472884382, 98154803250, 471644867446, 2270752198322, 10952481310992, 52912538251044, 256007757176486, 1240337826141202, 6016871820296958, 29221722675209464, 142071007529477192

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, j, 1 + 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: A258788 A100389 A151163 * A151165 A151166 A151167

Adjacent sequences: A151161 A151162 A151163 * A151165 A151166 A151167

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved