A148263 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, -1), (-1, 1, 1), (0, 1, 1), (1, -1, -1)}.

1, 1, 2, 4, 14, 33, 111, 323, 1150, 3550, 13232, 43213, 163571, 559092, 2153259, 7578945, 29644401, 106868221, 422484263, 1554283978, 6199956152, 23182015115, 93218237485, 353287504703, 1430209665244, 5484042065222, 22328830476538, 86484189896092, 353930565358679, 1382848864426607, 5684880552551872

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, 1 + 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, -1 + j, 1 + 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: A148260 A148261 A148262 * A148264 A148265 A148266

Adjacent sequences: A148260 A148261 A148262 * A148264 A148265 A148266

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved