A148026 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, 1, 0), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 3, 8, 17, 50, 123, 396, 1073, 3584, 10339, 35708, 108047, 382030, 1198693, 4313758, 13924021, 50809793, 167788571, 619059420, 2082876857, 7753892022, 26497831246, 99373513569, 344089136230, 1298396791328, 4546613757388, 17245911614695, 60979103246505, 232332342270363, 828469298335246, 3168602775158065

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + 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: A148024 A148025 A324615 * A148027 A148028 A148029

Adjacent sequences: A148023 A148024 A148025 * A148027 A148028 A148029

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved