A148973 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), (0, -1, 0), (0, 1, 1), (1, 1, -1)}.

1, 1, 3, 9, 32, 107, 401, 1510, 5995, 23717, 96670, 396096, 1654158, 6950924, 29542096, 126332499, 544511785, 2360468369, 10292596351, 45099988407, 198528103186, 877512440783, 3893476301675, 17335196172094, 77431700984140, 346889263547350, 1558334968896630, 7018378808999176, 31684707071734804

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, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, 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: A034540 A148971 A148972 * A148974 A148975 A148976

Adjacent sequences: A148970 A148971 A148972 * A148974 A148975 A148976

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved