A149227 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), (-1, 1, 1), (1, 1, -1), (1, 1, 0)}

1, 1, 4, 10, 46, 139, 667, 2269, 11056, 40420, 198622, 761287, 3761083, 14905342, 73897519, 300239101, 1492016545, 6179650609, 30758939461, 129359690452, 644617200640, 2744877878209, 13689374276287, 58893801473479, 293895276529510, 1275360122843992, 6367237075041664, 27834937991979418

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, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A155219 A153985 A184481 * A149228 A149229 A149230

Adjacent sequences: A149224 A149225 A149226 * A149228 A149229 A149230

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved