A148167 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, 1), (-1, 1, 0), (0, 0, 1), (0, 1, -1), (1, -1, 1)}.

1, 1, 2, 4, 11, 31, 101, 338, 1184, 4266, 15800, 59826, 231048, 906627, 3607644, 14528293, 59125375, 242878663, 1006043717, 4198395624, 17638730428, 74557621273, 316896467550, 1353741315715, 5809845607684, 25040550544405, 108350683436892, 470545685749693, 2050414447568200, 8962935331923249

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, 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, k, -1 + n] + aux[1 + i, 1 + 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: A213091 A148165 A148166 * A148168 A004251 A148169

Adjacent sequences: A148164 A148165 A148166 * A148168 A148169 A148170

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved