A149731 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, 1)}.

1, 1, 5, 17, 75, 295, 1355, 5735, 26889, 119049, 563877, 2559583, 12233685, 56509413, 271749707, 1271367259, 6142981385, 29011812723, 140710423527, 669480882365, 3256800002819, 15586963397677, 76014343698047, 365548011638983, 1786406716126545, 8624835338645779, 42223301114369687, 204533388015875227

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, -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: A149729 A282963 A149730 * A149732 A149733 A149734

Adjacent sequences: A149728 A149729 A149730 * A149732 A149733 A149734

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved