A150165 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, 0), (0, 0, 1), (1, -1, -1), (1, 1, 0)}.

1, 2, 6, 20, 75, 289, 1153, 4742, 19899, 84806, 365468, 1591554, 6991967, 30940027, 137761122, 616680344, 2773645233, 12527371702, 56790990386, 258307385503, 1178380844230, 5390151289483, 24715957334863, 113585243265110, 523060363963276, 2413206743521694, 11152858535263577, 51626269632904561

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, 1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A150162 A150163 A150164 * A148482 A383480 A148483

Adjacent sequences: A150162 A150163 A150164 * A150166 A150167 A150168

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved