A148727 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), (0, 1, 1), (1, 0, -1)}.

1, 1, 3, 7, 25, 72, 278, 918, 3678, 13008, 53788, 200502, 844075, 3258363, 13943192, 55340162, 239449624, 970569758, 4241711654, 17492540256, 77030015096, 322137728727, 1428245048087, 6043854822426, 26944775822220, 115160638548762, 515967003565501, 2224260898468260, 10007663318362161

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, j, 1 + k, -1 + n] + aux[i, -1 + 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: A309911 A148725 A148726 * A148728 A148729 A143339

Adjacent sequences: A148724 A148725 A148726 * A148728 A148729 A148730

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved