A148406 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, 0, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 5, 17, 52, 178, 641, 2403, 8988, 34682, 136929, 549249, 2208591, 9016463, 37266518, 155368761, 649397772, 2738792648, 11638862510, 49737875136, 212992280024, 917552497852, 3973132725054, 17271775610916, 75208605499383, 328884689265502, 1443554637089353, 6354561413054899

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, 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: A061675 A148405 A216969 * A148407 A141303 A263678

Adjacent sequences: A148403 A148404 A148405 * A148407 A148408 A148409

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved