A148969 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, 0), (0, 1, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 3, 9, 31, 109, 401, 1529, 5933, 23677, 96123, 393067, 1626847, 6802771, 28670115, 121927421, 521950931, 2244471413, 9701621923, 42139999533, 183851179889, 805623893623, 3542539051449, 15622274745531, 69096398821167, 306494968545683, 1363303054848177, 6079736450020545, 27172530115976509

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[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A189429 A123222 A148968 * A112566 A128082 A148970

Adjacent sequences: A148966 A148967 A148968 * A148970 A148971 A148972

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved