A149140 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, 0, 1), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 9, 36, 110, 440, 1485, 6138, 21902, 92050, 339946, 1446888, 5494374, 23538850, 91150203, 392888970, 1545871468, 6689452848, 26641201900, 115706733198, 465593151464, 2027309413796, 8225800678704, 35902335117164, 146733053157966, 641572595904506, 2638046749674882, 11553667215934304

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149137 A149138 A149139 * A239230 A149141 A149142

Adjacent sequences: A149137 A149138 A149139 * A149141 A149142 A149143

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved