A150062 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, 1), (-1, 0, 0), (0, 0, 1), (0, 1, -1), (1, 0, 0)}.

1, 2, 6, 18, 63, 223, 850, 3280, 13162, 53421, 221716, 929697, 3952869, 16954033, 73403606, 320088805, 1405405599, 6206513462, 27554351874, 122904959481, 550538683547, 2475553737317, 11170360194984, 50564231617795, 229552333182757, 1044915653862150, 4768147384522169, 21807532766531791

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[i, j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A150059 A150060 A150061 * A150063 A150064 A148463

Adjacent sequences: A150059 A150060 A150061 * A150063 A150064 A150065

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved