A150602 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), (0, 1, -1), (1, 0, 1), (1, 1, -1), (1, 1, 0)}.

1, 2, 7, 27, 110, 471, 2074, 9324, 42575, 196711, 917630, 4312657, 20395616, 96955941, 462904953, 2218328161, 10664452192, 51410836565, 248439068290, 1203124101905, 5837424744357, 28370263692593, 138089789041564, 673055239393798, 3284543508171306, 16046703767332874, 78476696861992508

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A150600 A005768 A150601 * A150603 A150604 A150605

Adjacent sequences: A150599 A150600 A150601 * A150603 A150604 A150605

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved