A150304 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, 0), (-1, 1, -1), (0, 0, 1), (1, 0, -1), (1, 0, 1)}.

1, 2, 7, 21, 82, 295, 1224, 4863, 20642, 86712, 375745, 1636141, 7224851, 32128224, 144099952, 650284953, 2955045582, 13489230967, 61907970108, 285216533074, 1319432538352, 6125687837276, 28528343584820, 133271278318064, 624219798528028, 2931203273847741, 13797068728422039, 65078551899506782

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A150301 A150302 A150303 * A150305 A150306 A150307

Adjacent sequences: A150301 A150302 A150303 * A150305 A150306 A150307

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved