A148922 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, 0, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 9, 26, 90, 323, 1129, 4241, 15991, 60977, 237469, 927444, 3673875, 14661668, 58676083, 237287338, 963042413, 3922169567, 16073137718, 66046964584, 272342523317, 1127073611456, 4675400296254, 19453051863408, 81131048704198, 339073462880469, 1420469270451043, 5961502961858243

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[1 + i, j, -1 + 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: A368088 A196952 A148921 * A148923 A058143 A126025

Adjacent sequences: A148919 A148920 A148921 * A148923 A148924 A148925

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved