A148174 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, 1, 1), (1, -1, 0)}.

1, 1, 2, 4, 12, 27, 84, 224, 712, 2006, 6662, 19530, 66075, 200809, 687115, 2142561, 7425605, 23578903, 82400432, 266087903, 936840796, 3062357204, 10851189800, 35873694160, 127705408346, 426238811147, 1524384589614, 5127606562685, 18409111458399, 62372449364233, 224664598203130, 765864853776425

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, k, -1 + n] + aux[i, -1 + 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: A027132 A148172 A148173 * A232218 A292065 A193893

Adjacent sequences: A148171 A148172 A148173 * A148175 A148176 A148177

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved