A148685 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, 1, -1), (1, 0, -1), (1, 1, 0)}.

1, 1, 3, 7, 22, 66, 227, 768, 2771, 10025, 37661, 142117, 548827, 2135363, 8429552, 33539945, 134793466, 545473164, 2224521240, 9126088552, 37669774713, 156291183756, 651703333129, 2729564106197, 11480817576072, 48475175596266, 205419727220096, 873413070037042, 3725364574591882

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 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: A148682 A148683 A148684 * A365452 A035353 A242566

Adjacent sequences: A148682 A148683 A148684 * A148686 A148687 A148688

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved