A148729 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, 1), (0, 0, -1), (0, 0, 1), (1, 1, -1)}.

1, 1, 3, 7, 25, 73, 281, 925, 3715, 13163, 54363, 202455, 852991, 3292995, 14084535, 55873491, 241813049, 979932617, 4281582977, 17650788629, 77729583213, 324985250073, 1440647882005, 6094701870121, 27170626608273, 116101605411245, 520124649045449, 2241711086478733, 10085665589693369

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, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A148726 A148727 A148728 * A143339 A148730 A148731

Adjacent sequences: A148726 A148727 A148728 * A148730 A148731 A148732

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved