A150087 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), (0, 0, -1), (0, 0, 1), (1, 0, 0)}.

1, 2, 6, 19, 66, 243, 929, 3676, 14808, 60805, 252986, 1065589, 4536809, 19477581, 84303710, 367160122, 1608825471, 7085704233, 31353847815, 139335954645, 621512821655, 2782177030111, 12492835133199, 56262640514675, 254057915721103, 1150053975016142, 5218025470526626, 23725098445219734

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, j, k, -1 + n] + aux[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, 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: A266466 A005654 A150086 * A150088 A150089 A150090

Adjacent sequences: A150084 A150085 A150086 * A150088 A150089 A150090

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved