A148676 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, 0, 0), (0, -1, 0), (0, 0, 1), (0, 1, -1), (1, 0, -1)}

1, 1, 3, 7, 21, 65, 209, 711, 2479, 8843, 32395, 120577, 455385, 1747389, 6778983, 26564107, 105215535, 420078017, 1689539809, 6848322853, 27927549903, 114530918967, 472483367857, 1958485189133, 8154314127735, 34110442991601, 143238416823021, 603675272939817, 2553859981719389

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, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, 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: A052805 A148674 A148675 * A105864 A130380 A097147

Adjacent sequences: A148673 A148674 A148675 * A148677 A148678 A148679

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved