A150828 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), (1, 0, 0), (1, 1, -1), (1, 1, 1)}.

1, 2, 8, 31, 146, 641, 3118, 14378, 70835, 335145, 1661438, 7981402, 39699537, 192584137, 959754642, 4686827981, 23384008468, 114732996836, 572848499697, 2820455568710, 14088682797586, 69549471921341, 347516935747050, 1719041818264667, 8591246204576259, 42566503795380074, 212763527638271061

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, 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: A150825 A150826 A150827 * A308336 A120774 A261052

Adjacent sequences: A150825 A150826 A150827 * A150829 A150830 A150831

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved