A151185 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, 1, -1), (1, 1, 0)}.

1, 3, 12, 51, 228, 1046, 4890, 23163, 110778, 533734, 2586338, 12590026, 61513848, 301461872, 1481094428, 7292017771, 35965507614, 177657952426, 878718765970, 4351160454886, 21566829418832, 106989157869960, 531153575115364, 2638691991990022, 13116334236443300, 65232346007880844, 324575450192664484

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, -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: A151184 A256334 A377582 * A151186 A151187 A340893

Adjacent sequences: A151182 A151183 A151184 * A151186 A151187 A151188

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved