A148758 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), (-1, 1, 1), (1, 0, -1), (1, 0, 0)}.

1, 1, 3, 7, 28, 81, 352, 1154, 5208, 18450, 85202, 317719, 1489930, 5762701, 27316040, 108584686, 518762827, 2106471761, 10123531026, 41810856886, 201869469476, 845355773410, 4096563483555, 17353296616714, 84345572763846, 360774559654579, 1757889969930777, 7581645820626841, 37018777212600691

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + 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: A352701 A351771 A148757 * A054277 A197960 A197959

Adjacent sequences: A148755 A148756 A148757 * A148759 A148760 A148761

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved