A150888 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1,0,1), (1,-1,1), (1,0,0), (1,1,-1), (1,1,1)}.

1, 2, 8, 33, 152, 703, 3363, 16123, 78405, 382031, 1874728, 9214167, 45464404, 224599699, 1112123401, 5511828827, 27357175892, 135878942511, 675540367558, 3360357589306, 16726611246327, 83293809912290, 414976379155574, 2068124206841016, 10310539526314684, 51416048094701054, 256466352906588744

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150885 A150886 A150887 * A256182 A030977 A030821

Adjacent sequences: A150885 A150886 A150887 * A150889 A150890 A150891

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved