A148557 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, 1, 0), (0, 0, -1), (0, 0, 1), (1, 0, -1)}.

1, 1, 3, 6, 18, 47, 146, 447, 1466, 4942, 16980, 60336, 215195, 789272, 2907758, 10919990, 41340269, 158282738, 612024510, 2382090777, 9361524557, 36969568871, 147194884001, 588824950464, 2370187980897, 9587635766815, 38961725380190, 159104026177375, 652087561742696, 2684530321305299

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A151262 A148555 A148556 * A148558 A148559 A108507

Adjacent sequences: A148554 A148555 A148556 * A148558 A148559 A148560

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved