A148307 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, 1), (0, 1, -1), (1, 0, -1), (1, 1, 0)}.

1, 1, 2, 5, 14, 37, 111, 365, 1126, 3763, 12701, 43975, 152390, 542045, 1940880, 7015549, 25755124, 94610231, 352061771, 1315135003, 4958004914, 18755194367, 71374096312, 272998723401, 1048508076514, 4048387313687, 15668442056095, 60926282586839, 237585820759632, 930052821537567, 3650378483240447

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, k, -1 + n] + aux[-1 + i, j, 1 + 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, 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: A143141 A117294 A148306 * A148308 A148309 A148310

Adjacent sequences: A148304 A148305 A148306 * A148308 A148309 A148310

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved