A151150 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, 1, -1), (0, 1, 1), (1, 0, 1), (1, 1, 0)}

1, 3, 11, 47, 205, 927, 4263, 19873, 93477, 443099, 2111677, 10111271, 48593723, 234274543, 1132435961, 5486484089, 26633535227, 129513967703, 630765345243, 3076177529709, 15020545826403, 73424228430541, 359275730715121, 1759596267979597, 8625046993876771, 42310103527742087, 207699373802231315

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[1 + i, -1 + 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: A151147 A151148 A151149 * A151151 A151152 A151153

Adjacent sequences: A151147 A151148 A151149 * A151151 A151152 A151153

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved