A147999 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), (-1, 1, 0), (1, 0, 0)}.

1, 1, 2, 3, 8, 15, 39, 77, 244, 543, 1655, 3729, 12385, 29510, 93170, 221283, 764948, 1908675, 6323115, 15688889, 55069789, 141067986, 473165330, 1200395415, 4290381497, 11232104990, 38585190644, 100082744787, 360316046969, 956558534943, 3305432502421, 8679121868177, 31575545872868, 84905308145331

Offset

0,3

Links

Table of n, a(n) for n=0..33.

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, k, -1 + n] + aux[1 + i, -1 + j, 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: A308433 A049957 A151255 * A148000 A148001 A148002

Adjacent sequences: A147996 A147997 A147998 * A148000 A148001 A148002

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved