A150950 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, 1)}.

1, 2, 9, 35, 155, 677, 3095, 14118, 65638, 305990, 1441145, 6806351, 32340167, 154078157, 737054642, 3533761685, 16991087801, 81854181707, 395188982837, 1911028600311, 9256966504941, 44901779898247, 218101345032323, 1060615097938213, 5163621825820379, 25164338852297569, 122754470830849509

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, -1 + 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: A363549 A150948 A150949 * A150951 A150952 A150953

Adjacent sequences: A150947 A150948 A150949 * A150951 A150952 A150953

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved