A149730 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, 0, 1), (1, 0, -1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 75, 295, 1349, 5729, 26757, 118527, 560259, 2546099, 12144117, 56151281, 269644087, 1262417629, 6093239571, 28796251075, 139545443435, 664306612693, 3229548391107, 15463843514919, 75375535979473, 362624920462911, 1771412430257817, 8555451112575391, 41870416595861169, 202886096194456097

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, 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: A149728 A149729 A282963 * A149731 A149732 A149733

Adjacent sequences: A149727 A149728 A149729 * A149731 A149732 A149733

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved