A148813 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, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 26, 86, 314, 1113, 4239, 16219, 63071, 248619, 1006515, 4029015, 16543263, 68254132, 282375694, 1178569272, 4977684152, 20904474572, 88923131344, 379777454862, 1621498075454, 6967327961546, 30135682169814, 129893637023738, 564250514132646, 2459005713673728, 10704199214707220

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, 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: A148810 A148811 A148812 * A369618 A148814 A161938

Adjacent sequences: A148810 A148811 A148812 * A148814 A148815 A148816

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved