A148178 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), (-1, 1, -1), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 4, 12, 28, 91, 242, 839, 2416, 8782, 26700, 100437, 317981, 1226766, 4010820, 15782053, 52955735, 211754709, 725756163, 2941028924, 10260046434, 42043257062, 148908505647, 615994366991, 2210482944544, 9219230935633, 33462915243756, 140563142274370, 515352054090757, 2178406144490742

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, k, -1 + n] + aux[-1 + i, 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, 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: A148176 A148177 A080876 * A148179 A148180 A148181

Adjacent sequences: A148175 A148176 A148177 * A148179 A148180 A148181

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved