A148841 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), (0, 1, -1), (0, 1, 1), (1, -1, 0)}.

1, 1, 3, 8, 27, 93, 330, 1225, 4748, 18254, 72864, 295766, 1202739, 4982093, 20818757, 87599870, 371843504, 1586274436, 6819658928, 29475046107, 127741159201, 557407746280, 2441739857808, 10717447515735, 47285645164133, 209257398094743, 927976766078263, 4130130549335293, 18424601220048862

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[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: A281347 A000238 A259811 * A148842 A330783 A148843

Adjacent sequences: A148838 A148839 A148840 * A148842 A148843 A148844

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved