A150604 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, 1), (0, 1, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 27, 110, 472, 2079, 9353, 42739, 197615, 922243, 4336704, 20517659, 97571226, 465996270, 2233748351, 10741244740, 51791965769, 250327475997, 1212466550103, 5883588623168, 28598192874099, 139214373132978, 678601421552300, 3311886380405507, 16181475316087873, 79140892444806360

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150601 A150602 A150603 * A150605 A150606 A150607

Adjacent sequences: A150601 A150602 A150603 * A150605 A150606 A150607

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved