A150935 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), (1, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 33, 159, 671, 3288, 14719, 72664, 335880, 1664988, 7849149, 39004188, 186294948, 927213201, 4469530443, 22269520555, 108073079585, 538890342551, 2628561459138, 13114310579949, 64221071659033, 320544468838524, 1574624610642784, 7861912554105647, 38717644728189914, 193361258767889412

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, -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: A150932 A150933 A150934 * A150936 A109719 A263685

Adjacent sequences: A150932 A150933 A150934 * A150936 A150937 A150938

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved