A148867 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), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 29, 90, 338, 1136, 4364, 15310, 59572, 214262, 840471, 3078526, 12139887, 45044594, 178241996, 667774177, 2648963397, 9999689992, 39738357610, 150915750913, 600537722260, 2291965479255, 9129724083081, 34986605091307, 139473129727091, 536326148856237, 2139361142887059

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, j, -1 + 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: A195687 A060707 A080874 * A063546 A148868 A148869

Adjacent sequences: A148864 A148865 A148866 * A148868 A148869 A148870

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved