A148474 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, 0, 1), (1, 1, -1)}.

1, 1, 2, 6, 20, 65, 241, 889, 3472, 13622, 55340, 225557, 940725, 3937330, 16738031, 71404967, 307999065, 1332931401, 5815439839, 25450058722, 112060278048, 494798567807, 2195172975521, 9763509301815, 43589884062136, 195052842541424, 875498008541850, 3937713690439906, 17755851945737789

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, 1 + k, -1 + n] + aux[i, 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: A005726 A148473 A000718 * A156831 A027061 A279460

Adjacent sequences: A148471 A148472 A148473 * A148475 A148476 A148477

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved