A148511 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, 0, 0), (-1, 1, 0), (0, 0, -1), (1, 0, 0)}.

1, 1, 3, 5, 17, 36, 128, 320, 1140, 3246, 11434, 35916, 125474, 422089, 1477804, 5192274, 18397703, 66315629, 239082564, 875153486, 3212013856, 11889752467, 44309767139, 165710641660, 624879419948, 2360913501837, 8983291298866, 34272210640140, 131379922642520, 505553595407305, 1951228119370848

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A148510 A215396 A130844 * A148512 A148513 A148514

Adjacent sequences: A148508 A148509 A148510 * A148512 A148513 A148514

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved