A148666 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, 1, -1), (-1, 1, 1), (1, -1, -1), (1, 0, 1)}

1, 1, 3, 6, 26, 67, 289, 883, 3939, 12973, 59283, 206203, 953701, 3457009, 16139619, 60317808, 283794508, 1086268906, 5141489214, 20066470430, 95428374560, 378479119402, 1807009062046, 7264063813212, 34797461658262, 141500592207376, 679764959958540, 2791786769009805, 13444463152291645

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, 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, 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: A197470 A148664 A148665 * A058258 A215397 A359974

Adjacent sequences: A148663 A148664 A148665 * A148667 A148668 A148669

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved