A148910 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), (1, -1, 0), (1, 0, -1), (1, 0, 0)}.

1, 1, 3, 8, 32, 107, 459, 1745, 7791, 31799, 145590, 621868, 2895091, 12756232, 60094306, 270756085, 1286759098, 5894676721, 28202824567, 130855990876, 629384181850, 2949636100403, 14247198887620, 67308391223347, 326237806867709, 1551368825330913, 7541011224240539, 36054388380082394

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, 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, 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: A148907 A148908 A148909 * A148911 A148912 A148913

Adjacent sequences: A148907 A148908 A148909 * A148911 A148912 A148913

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved