A151052 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, 0), (0, 0, 1), (0, 1, 0), (1, 1, 0)}.

1, 3, 10, 37, 144, 579, 2388, 10034, 42776, 184515, 803609, 3528235, 15597277, 69359086, 310019528, 1391987818, 6275072316, 28389123237, 128847871383, 586488987180, 2676603498328, 12244738097206, 56139530483881, 257908182355785, 1187054906742932, 5473003937362030, 25274142877986714

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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A151051 A164044 A119244 * A264231 A151053 A151054

Adjacent sequences: A151049 A151050 A151051 * A151053 A151054 A151055

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved