A148323 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, 0, 0), (-1, 1, 1), (0, -1, 1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 5, 14, 41, 134, 451, 1579, 5725, 21247, 80532, 311203, 1220208, 4851662, 19519760, 79346540, 325592275, 1347098177, 5615181079, 23565529525, 99503559928, 422509407783, 1803261895238, 7732529216295, 33302199102857, 144001008471676, 624992627998857, 2722004649269076

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, 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, 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: A243870 A287968 A148322 * A148324 A000660 A148325

Adjacent sequences: A148320 A148321 A148322 * A148324 A148325 A148326

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved