A150027 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, -1, 1), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 5, 19, 74, 298, 1281, 5462, 24099, 108077, 487391, 2236789, 10301023, 47843041, 223735126, 1049895022, 4956915448, 23474704967, 111584020732, 532185167879, 2544210999914, 12197908389471, 58601743861377, 282127456392257, 1360861827426384, 6574796619320823, 31817366089923143, 154187495072008827

Offset

0,2

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, k, -1 + n] + aux[1 + i, 1 + 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: A014273 A255541 A150026 * A277969 A058131 A222055

Adjacent sequences: A150024 A150025 A150026 * A150028 A150029 A150030

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved