A148799 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, 0, -1), (0, 1, 1), (1, -1, 0)}.

1, 1, 3, 8, 25, 86, 294, 1024, 3817, 14242, 54008, 208696, 811078, 3195510, 12739105, 50994738, 205890076, 836663641, 3415423985, 14032729088, 57915331555, 239929351225, 998341477817, 4168025001135, 17460273027901, 73393532119090, 309339627471817, 1307340906252813, 5539469603511181

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, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A000738 A006372 A148798 * A148800 A244278 A373175

Adjacent sequences: A148796 A148797 A148798 * A148800 A148801 A148802

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved