A149852 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, 1, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 4, 14, 46, 154, 578, 2168, 8182, 31532, 125070, 493576, 1967344, 7989243, 32449575, 132284139, 544422926, 2252015827, 9319866551, 38789146879, 162226732758, 679162610573, 2851506701472, 12018168463717, 50743114587121, 214563325115979, 909819286375420, 3865266727785403

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A149850 A255502 A149851 * A263740 A005437 A214267

Adjacent sequences: A149849 A149850 A149851 * A149853 A149854 A149855

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved