A148071 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), (1, 0, 0)}.

1, 1, 2, 4, 9, 21, 51, 143, 374, 1071, 3095, 8934, 26170, 77812, 239576, 719583, 2245728, 7027771, 21874554, 68780246, 217957471, 699596665, 2221050242, 7204830752, 23364983444, 75490995551, 245743450650, 803146080439, 2641243592039, 8638752159115, 28638848337491, 94831340109958, 313328526209055

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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[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: A230556 A027057 A333105 * A000636 A204352 A195980

Adjacent sequences: A148068 A148069 A148070 * A148072 A148073 A148074

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved