A148637 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, 0), (1, -1, -1), (1, 1, -1), (1, 1, 0)}.

1, 1, 3, 6, 22, 61, 227, 721, 2787, 9666, 38536, 140765, 573595, 2173584, 9013346, 35145343, 147772519, 589214977, 2505119741, 10168189527, 43634082045, 179723654395, 777338999095, 3241360071695, 14114448460883, 59471929264838, 260488476345462, 1107469740827593, 4875700267229383

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A323924 A148635 A148636 * A148638 A148639 A148640

Adjacent sequences: A148634 A148635 A148636 * A148638 A148639 A148640

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved