A148149 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, 0, 1), (1, -1, -1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 11, 29, 97, 300, 1077, 3634, 13653, 49031, 190864, 716619, 2864542, 11113948, 45338516, 180423941, 748010246, 3037549738, 12759948361, 52676833687, 223710004285, 936214898900, 4012733348896, 16986312988164, 73381258658937, 313666205814135, 1364316375158136, 5880681766872382

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A148147 A298269 A148148 * A034769 A219017 A285216

Adjacent sequences: A148146 A148147 A148148 * A148150 A148151 A148152

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved