A149606 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, 1)}

1, 1, 5, 15, 61, 237, 975, 4081, 17261, 74547, 322841, 1420107, 6261387, 27888709, 124625769, 560265961, 2528574721, 11451972219, 52069274841, 237281726121, 1085084024061, 4970662739891, 22836062726627, 105075942293149, 484587271695233, 2238189819488845, 10355635839588187, 47984258936384387

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, -1 + j, -1 + k, -1 + 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: A149603 A149604 A149605 * A363466 A019045 A191678

Adjacent sequences: A149603 A149604 A149605 * A149607 A149608 A149609

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved