A150801 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, 1, 0), (0, 0, 1), (1, 0, -1), (1, 1, 1)}.

1, 2, 8, 31, 132, 572, 2567, 11697, 54085, 252536, 1188950, 5632253, 26822989, 128295939, 615915211, 2966142385, 14323235723, 69328421550, 336263280061, 1633951973489, 7952500232382, 38761246008431, 189172446314111, 924334974428614, 4521317400249156, 22137241967117701, 108484807021732176

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, -1 + 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: A150798 A150799 A150800 * A150802 A150803 A150804

Adjacent sequences: A150798 A150799 A150800 * A150802 A150803 A150804

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved