A149724 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, 1), (0, 0, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 75, 285, 1317, 5567, 25985, 114405, 542049, 2456039, 11720847, 54060867, 259872549, 1214918367, 5866220625, 27689646713, 134259837463, 638654468767, 3105757823623, 14861570751109, 72466412558809, 348482332573211, 1702720911060097, 8220802950971551, 40243093261609041, 194955190455663275

Offset

0,3

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, 1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A362177 A102387 A149723 * A149725 A149726 A149727

Adjacent sequences: A149721 A149722 A149723 * A149725 A149726 A149727

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved