A149037 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, 0), (-1, 0, 1), (0, 1, 1), (1, -1, 1), (1, 0, -1)}.

1, 1, 3, 10, 35, 128, 507, 2018, 8233, 34330, 144621, 616132, 2653433, 11506566, 50254573, 220854412, 975469382, 4328974934, 19292389001, 86294255900, 387314440619, 1743745017299, 7872524977741, 35634378681771, 161678959915454, 735169254989379, 3349694058675870, 15291239270252546

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A299443 A128736 A303730 * A228769 A361768 A296164

Adjacent sequences: A149034 A149035 A149036 * A149038 A149039 A149040

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved