A149933 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, 1, 0), (1, 0, 0)}.

1, 2, 5, 15, 49, 165, 584, 2134, 7930, 30004, 115286, 448041, 1758361, 6960484, 27766468, 111490323, 450177914, 1827430423, 7453136569, 30521419571, 125469410644, 517600974331, 2141983544608, 8890103668822, 36997531250241, 154355482106971, 645473861118404, 2705027636972910

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, -1 + j, 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: A190908 A149931 A149932 * A149934 A348666 A149935

Adjacent sequences: A149930 A149931 A149932 * A149934 A149935 A149936

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved