A151168 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), (0, 1, 1), (1, 0, 1)}

1, 3, 12, 48, 213, 951, 4359, 20208, 94758, 447624, 2127430, 10163516, 48750957, 234641671, 1132668361, 5481238693, 26582499057, 129161103024, 628628768670, 3064072780333, 14954732374754, 73076156906414, 357470266540334, 1750365483692510, 8578371955284307, 42076139729259151, 206534763492110897

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, j, -1 + k, -1 + n] + aux[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, 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: A351282 A142873 A301578 * A151169 A058371 A226443

Adjacent sequences: A151165 A151166 A151167 * A151169 A151170 A151171

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved