A148115 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, 0, 1), (0, 1, -1), (1, -1, 1), (1, 0, 0)}.

1, 1, 2, 4, 10, 30, 89, 292, 979, 3400, 12343, 45414, 171339, 658069, 2563330, 10148718, 40637220, 164466898, 672375792, 2772055955, 11523056929, 48249869722, 203337220125, 862137480843, 3675561131454, 15750515059157, 67817588931961, 293278774651265, 1273450290226531, 5550464963189884

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, 1 + 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, 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: A361791 A102667 A337675 * A361758 A148116 A149833

Adjacent sequences: A148112 A148113 A148114 * A148116 A148117 A148118

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved