A148460 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, 0), (0, 0, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 6, 18, 59, 210, 767, 2901, 11295, 44756, 180348, 738130, 3057350, 12789793, 54032745, 230170481, 987155382, 4262047055, 18511560553, 80808289797, 354440593530, 1561601787236, 6907093680245, 30660957686730, 136574647572439, 610247973013998, 2734489839406472, 12286433733748477

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, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A036675 A227373 A121320 * A148461 A358251 A002527

Adjacent sequences: A148457 A148458 A148459 * A148461 A148462 A148463

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved