A148432 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), (0, 1, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 5, 19, 61, 231, 829, 3411, 13174, 55582, 224050, 967760, 4025392, 17659214, 75079047, 333251508, 1441084386, 6455852339, 28282925801, 127631409983, 565049348637, 2565238396179, 11453873093860, 52258674096405, 234993625412768, 1076697344305840, 4870486794682944, 22396424337542850

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, 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, 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: A148431 A321006 A320276 * A047116 A148433 A148434

Adjacent sequences: A148429 A148430 A148431 * A148433 A148434 A148435

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved