A151179 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, 0)}.

1, 3, 12, 50, 223, 1015, 4729, 22313, 106417, 511458, 2473148, 12017294, 58620251, 286873813, 1407618180, 6922313041, 34106536761, 168315924156, 831793119344, 4115539692326, 20384128657815, 101054234497267, 501378809307513, 2489348020547553, 12367402039498161, 61477248248504698, 305750636377131818

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, 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: A119976 A074547 A151178 * A191242 A105479 A151180

Adjacent sequences: A151176 A151177 A151178 * A151180 A151181 A151182

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved