A148350 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), (1, 0, -1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 5, 15, 42, 141, 454, 1636, 5654, 21372, 77839, 304105, 1149623, 4605049, 17911778, 73142360, 290931536, 1206443012, 4886121626, 20518294930, 84344339293, 357919513388, 1489741008146, 6378159512931, 26830071268609, 115748486759273, 491362556375669, 2133872051606574

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[-1 + i, j, k, -1 + n] + aux[-1 + i, 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: A190140 A006649 A303980 * A304201 A215448 A094176

Adjacent sequences: A148347 A148348 A148349 * A148351 A148352 A148353

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved