A150597 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), (-1, 0, 0), (0, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 2, 7, 27, 108, 459, 1994, 8804, 39668, 180345, 828261, 3835665, 17869380, 83746921, 394258798, 1863940882, 8844326213, 42094388136, 200934619614, 961528165333, 4611556549374, 22163105762414, 106712056107950, 514676230609664, 2486127145587815, 12026281544464482, 58251743422904915, 282493832836296113

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A150595 A150596 A026726 * A150598 A026759 A361778

Adjacent sequences: A150594 A150595 A150596 * A150598 A150599 A150600

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved