A149270 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, 1), (0, 0, -1), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 11, 41, 148, 581, 2298, 9414, 39020, 164742, 702845, 3031984, 13191615, 57837324, 255216761, 1132838932, 5053711738, 22647339728, 101905858689, 460213087530, 2085199217472, 9476513961459, 43185037964172, 197289709201004, 903402441704377, 4145508982924713, 19060139964446839

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A030981 A151455 A149269 * A306188 A307702 A214167

Adjacent sequences: A149267 A149268 A149269 * A149271 A149272 A149273

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved