A150258 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, 1, 0), (0, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 22, 86, 358, 1532, 6738, 30142, 136742, 627494, 2904854, 13552541, 63619497, 300280369, 1423783749, 6778027336, 32379599861, 155157977040, 745514606550, 3590793187709, 17332744476921, 83828753578163, 406150158687018, 1970958831204045, 9578651423835851, 46613623400480035, 227119976189465826

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A277222 A150256 A150257 * A073075 A299021 A153475

Adjacent sequences: A150255 A150256 A150257 * A150259 A150260 A150261

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved