A148407 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, 0, 1), (0, 0, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 2, 5, 17, 52, 178, 650, 2429, 9195, 35763, 143627, 575774, 2347671, 9720885, 40634851, 170480202, 723016389, 3094415599, 13279927487, 57328187446, 249153610779, 1087747624310, 4760553453421, 20940649603780, 92505362953435, 409597553684849, 1818973443599400, 8107263431104032

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, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A148405 A216969 A148406 * A141303 A263678 A133510

Adjacent sequences: A148404 A148405 A148406 * A148408 A148409 A148410

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved