A150650 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, 1), (0, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 28, 118, 517, 2324, 10621, 49203, 230146, 1085409, 5149462, 24559846, 117620800, 565339017, 2725491522, 13174056237, 63823083626, 309812004803, 1506535878227, 7337290499538, 35784580416650, 174742448270302, 854261648133653, 4180496059111100, 20477164205120029, 100388139051441278

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, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A150648 A150649 A090317 * A150651 A151298 A161944

Adjacent sequences: A150647 A150648 A150649 * A150651 A150652 A150653

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved