A149274 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, 0), (1, -1, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 11, 42, 149, 604, 2335, 9813, 39940, 171681, 722028, 3154730, 13567418, 60004023, 262309602, 1171110162, 5183089316, 23316172437, 104193685265, 471628178813, 2123944521094, 9663820999334, 43796697446174, 200148890672519, 911873107494108, 4182970725344601, 19142531763842047

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A149271 A149272 A149273 * A151427 A149275 A378830

Adjacent sequences: A149271 A149272 A149273 * A149275 A149276 A149277

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved