A148812 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, -1, -1), (1, 0, 1)}.

1, 1, 3, 8, 26, 86, 309, 1112, 4300, 16355, 64610, 258460, 1049577, 4289188, 17767640, 74236553, 312798334, 1323001687, 5645624363, 24239460347, 104391408045, 451959306066, 1967440956925, 8589297566724, 37631972874233, 165505946315394, 730191658379518, 3230280805363359, 14327178302247607

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + 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: A151457 A148810 A148811 * A148813 A369618 A148814

Adjacent sequences: A148809 A148810 A148811 * A148813 A148814 A148815

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved