A149297 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, 0, -1), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 11, 46, 163, 691, 2761, 11734, 50199, 218371, 964109, 4274622, 19172727, 86702998, 393870617, 1804068528, 8280505767, 38258694113, 177369807157, 825171442348, 3854248987491, 18039911515304, 84739900425283, 398932218327032, 1882432029832379, 8904366161915705, 42187531241280899

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, j, 1 + k, -1 + n] + aux[i, 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: A149294 A149295 A149296 * A149298 A149299 A149300

Adjacent sequences: A149294 A149295 A149296 * A149298 A149299 A149300

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved