A148455 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, 1), (-1, 1, 1), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 6, 18, 54, 189, 633, 2304, 8304, 31165, 117040, 450812, 1738597, 6832754, 26873783, 107237479, 428294527, 1729570438, 6992686966, 28512482373, 116421902463, 478533610040, 1969894917140, 8152045246384, 33786980247672, 140634663815895, 586246071077852, 2452450863163104

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, 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, 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: A363432 A086680 A275872 * A094590 A004529 A366550

Adjacent sequences: A148452 A148453 A148454 * A148456 A148457 A148458

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved