A151117 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), (0, 1, 0), (1, 0, 0), (1, 1, 1)}.

1, 3, 11, 45, 193, 851, 3839, 17545, 81109, 378176, 1775372, 8381349, 39755815, 189318190, 904620647, 4335361919, 20830715266, 100316712526, 484090425939, 2340280824152, 11332374557823, 54956514211266, 266872363052541, 1297550327440948, 6315932371588958, 30775419199757426, 150103074713621374

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 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: A363183 A151115 A151116 * A151118 A151119 A151120

Adjacent sequences: A151114 A151115 A151116 * A151118 A151119 A151120

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved