A148884 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, -1), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 30, 97, 389, 1441, 5889, 23616, 99002, 413417, 1776811, 7615131, 33341337, 145808687, 647319019, 2875484141, 12912706883, 58054041349, 263234386877, 1194949733310, 5462241787614, 24996707232914, 115041699718214, 530075704218794, 2453825498716578, 11372606980198438, 52914248724872906

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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148881 A148882 A148883 * A148885 A148886 A148887

Adjacent sequences: A148881 A148882 A148883 * A148885 A148886 A148887

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved