A149042 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, 1, 1), (0, 1, -1), (1, -1, 1), (1, 0, 1)}.

1, 1, 3, 10, 36, 139, 567, 2354, 10051, 43745, 192742, 858883, 3869637, 17569721, 80307106, 369430312, 1708635040, 7938060632, 37034246311, 173437700581, 814901766911, 3840290612220, 18148048110860, 85975458675768, 408225045863473, 1942410972814486, 9260276749410251, 44226028788343006

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A202834 A129247 A162162 * A081921 A353262 A165792

Adjacent sequences: A149039 A149040 A149041 * A149043 A149044 A149045

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved