A148002 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), (-1, 1, -1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 3, 8, 15, 39, 87, 282, 717, 2145, 5807, 18226, 50197, 152504, 466049, 1518118, 4645813, 14702657, 46857147, 150247490, 470691795, 1534124568, 5119363053, 16980777560, 55558457979, 184820922541, 617405147985, 2039835934044, 6784928795159, 23153051794787, 79347944648053, 268928260995546

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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[i, j, -1 + k, -1 + n] + aux[1 + 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: A147999 A148000 A148001 * A148003 A148004 A300443

Adjacent sequences: A147999 A148000 A148001 * A148003 A148004 A148005

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved