A150234 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), (1, 0, -1), (1, 1, 0)}.

1, 2, 6, 22, 82, 329, 1356, 5728, 24771, 108333, 480976, 2155838, 9745021, 44411257, 203558361, 938658857, 4349164000, 20238009107, 94557029374, 443272736527, 2084784929706, 9832969315029, 46497685752388, 220411927241557, 1047065731564630, 4984265950513456, 23770506968527747, 113559811107454136

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, 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: A150231 A150232 A150233 * A150235 A150236 A068946

Adjacent sequences: A150231 A150232 A150233 * A150235 A150236 A150237

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved