A148004 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), (-1, 1, -1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 3, 8, 15, 39, 97, 302, 817, 2435, 7105, 21500, 63697, 206038, 663263, 2159140, 6975073, 23040857, 75117391, 251186106, 855285955, 2942402740, 10063076773, 34691521836, 119449516957, 413353318719, 1448193096705, 5134958790412, 18208618646053, 64646350213523, 229783838224857, 817714839981072

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148001 A148002 A148003 * A300443 A321231 A156802

Adjacent sequences: A148001 A148002 A148003 * A148005 A148006 A148007

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved