A151180 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, 0), (0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, -1)}

1, 3, 12, 50, 227, 1047, 4939, 23571, 113575, 550785, 2685286, 13143538, 64538881, 317716079, 1567357416, 7745417246, 38330815841, 189923526167, 942013070950, 4676466466360, 23233166431451, 115500619414161, 574524637022633, 2859238829041077, 14235846954865105, 70906304719276783, 353293684393014734

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A151179 A191242 A105479 * A268650 A151181 A094601

Adjacent sequences: A151177 A151178 A151179 * A151181 A151182 A151183

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved