A148289 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), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 5, 13, 34, 102, 304, 925, 2930, 9314, 30227, 99654, 329616, 1106171, 3739369, 12717657, 43624104, 150207317, 520337650, 1811959226, 6331767583, 22228799924, 78284646709, 276640110054, 980924228341, 3486919529824, 12430652320859, 44419798994329, 159093066856160, 571130418694862, 2054173729933912

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[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: A186236 A064780 A368599 * A148290 A029885 A114298

Adjacent sequences: A148286 A148287 A148288 * A148290 A148291 A148292

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved