A148145 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, 0, 1), (0, 0, 1), (0, 1, -1), (1, -1, 1)}.

1, 1, 2, 4, 11, 29, 88, 263, 849, 2723, 9157, 30722, 106294, 367742, 1299180, 4595014, 16493712, 59306116, 215549417, 784975686, 2881728074, 10600876580, 39237430745, 145524254095, 542325039961, 2024973907989, 7590098952820, 28500892031086, 107355932684246, 405060263789931, 1532269008006369

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A148142 A148143 A148144 * A052869 A316768 A052831

Adjacent sequences: A148142 A148143 A148144 * A148146 A148147 A148148

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved