A149864 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), (0, 0, 1), (0, 1, 0), (1, -1, 0)}.

1, 2, 5, 13, 40, 131, 452, 1562, 5644, 20799, 78589, 297261, 1148443, 4476655, 17703933, 70069434, 280865518, 1131469211, 4601137351, 18721075331, 76825846434, 316282614821, 1310738384205, 5434178009491, 22669009843172, 94776209742645, 398203425052616, 1673579306464051, 7066742149099808

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, k, -1 + n] + aux[i, 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: A371714 A291614 A202153 * A149865 A174146 A149866

Adjacent sequences: A149861 A149862 A149863 * A149865 A149866 A149867

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved