A148836 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, -1, 1)}.

1, 1, 3, 8, 27, 90, 314, 1128, 4153, 15645, 59702, 230787, 903001, 3564992, 14204743, 57014847, 230396765, 936783710, 3828965482, 15730767884, 64921356490, 269039650977, 1119245234734, 4672527853961, 19571504860039, 82229213110248, 346464646169936, 1463723358626057, 6199295747914251

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[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: A145792 A148834 A148835 * A148837 A148838 A148839

Adjacent sequences: A148833 A148834 A148835 * A148837 A148838 A148839

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved