A149155 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), (-1, 0, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 9, 39, 112, 512, 1660, 7778, 27188, 129401, 475825, 2288259, 8728352, 42284402, 165826745, 807712214, 3237235537, 15833338030, 64579379484, 316882110960, 1311217629144, 6450625830056, 27015741085305, 133185518215086, 563537265001788, 2783016272151599, 11879828894712115, 58753259096839334

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, j, 1 + k, -1 + n] + aux[1 + 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: A149153 A101529 A149154 * A149156 A149157 A149158

Adjacent sequences: A149152 A149153 A149154 * A149156 A149157 A149158

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved