A148621 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, 1, -1), (0, 1, 1), (1, -1, -1)}.

1, 1, 3, 6, 21, 59, 215, 687, 2674, 9218, 36708, 134191, 548938, 2074773, 8638690, 33714423, 142274466, 566710795, 2422552226, 9835927336, 42399780851, 174675742734, 759821784189, 3169417373597, 13873062381715, 58502587257970, 257705474537922, 1096405761031918, 4854199110479186

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + 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: A148618 A148619 A148620 * A148622 A148623 A259273

Adjacent sequences: A148618 A148619 A148620 * A148622 A148623 A148624

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved