A148211 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, 0, 1), (-1, 1, 1), (0, 0, 1), (0, 1, -1), (1, -1, 1)}.

1, 1, 2, 4, 12, 36, 123, 422, 1556, 5797, 22512, 88244, 355082, 1441038, 5951551, 24763384, 104316842, 442258945, 1892124241, 8139630740, 35259782511, 153461173363, 671582239139, 2950933397118, 13024116086453, 57684461929497, 256428223442345, 1143394392156529, 5114133402269907

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[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, 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: A048116 A148209 A148210 * A369688 A009152 A081443

Adjacent sequences: A148208 A148209 A148210 * A148212 A148213 A148214

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved