A149932 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, 0, -1), (-1, 1, 1), (0, 0, 1), (1, 0, 0)}.

1, 2, 5, 15, 49, 165, 584, 2134, 7902, 29892, 114882, 445389, 1746830, 6917227, 27555548, 110577812, 446571878, 1811419809, 7384904017, 30243833998, 124275887253, 512565470691, 2121206098773, 8801749477275, 36626130235013, 152811471519802, 638933029743026, 2677526963798012

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[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A360233 A190908 A149931 * A149933 A149934 A348666

Adjacent sequences: A149929 A149930 A149931 * A149933 A149934 A149935

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved