A151038 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), (0, 1, 1), (1, 0, 1), (1, 1, 0)}.

1, 3, 9, 33, 123, 459, 1767, 6795, 26397, 103323, 404439, 1591917, 6274389, 24780489, 98110263, 388610895, 1541837565, 6122129877, 24327902433, 96767761083, 385038905697, 1533118174923, 6107008497819, 24335988943143, 97021648253361, 386885931518703, 1543276950241995, 6157531782523065

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + 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: A255713 A148997 A082841 * A039648 A307454 A219261

Adjacent sequences: A151035 A151036 A151037 * A151039 A151040 A151041

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved