A148437 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, 1), (0, 1, 0), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 5, 19, 67, 288, 1151, 5166, 21993, 101298, 448645, 2103115, 9563057, 45376178, 210129929, 1005672823, 4718671583, 22726455310, 107680660715, 521111158087, 2487628072793, 12083759630094, 58023822038299, 282697015830760, 1363850749566431, 6661019969496358, 32258912674456581, 157870992453432227

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, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A148435 A047022 A148436 * A106873 A014273 A255541

Adjacent sequences: A148434 A148435 A148436 * A148438 A148439 A148440

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved