A148475 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), (0, -1, 1), (0, 0, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 2, 6, 20, 67, 236, 878, 3371, 13228, 52874, 214793, 885291, 3692585, 15554663, 66101794, 283128271, 1221159525, 5299556530, 23126058386, 101422704683, 446830641450, 1976714921695, 8777773858617, 39113829187673, 174849134753900, 783932609596663, 3524370330304937, 15885021252427176

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[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[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: A108627 A193234 A285197 * A148476 A148477 A369123

Adjacent sequences: A148472 A148473 A148474 * A148476 A148477 A148478

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved