A148442 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), (-1, 1, 0), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 6, 16, 46, 155, 501, 1686, 5991, 21017, 76040, 280654, 1035640, 3896052, 14780804, 56362934, 217403028, 842891300, 3286540585, 12904895803, 50886586718, 201628355072, 802775113349, 3207600418058, 12866424867935, 51798254861305, 209156221493593, 847252559115452, 3441859987736618

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, -1 + j, -1 + k, -1 + n] + aux[1 + 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: A165431 A182267 A003291 * A190729 A071726 A148443

Adjacent sequences: A148439 A148440 A148441 * A148443 A148444 A148445

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved