A150625 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, 0, 1), (0, 1, 0), (1, -1, 1), (1, 0, -1), (1, 0, 1)}.

1, 2, 7, 27, 113, 492, 2199, 10018, 46265, 215978, 1016645, 4817665, 22954305, 109859680, 527770605, 2543501545, 12291399297, 59537652888, 288982816863, 1405186305829, 6843636407627, 33377608304614, 162995021994673, 796873495176386, 3899896598283489, 19104013268330962, 93663070141612901

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A150622 A150623 A150624 * A150626 A150627 A150628

Adjacent sequences: A150622 A150623 A150624 * A150626 A150627 A150628

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved