A148840 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), (-1, 0, 0), (0, -1, 1), (0, 1, 1), (1, 0, -1)}.

1, 1, 3, 8, 27, 90, 319, 1167, 4393, 16770, 65667, 261142, 1049235, 4251083, 17422677, 71909371, 298913230, 1251993805, 5278397210, 22349721983, 95054794883, 406143454387, 1742036880493, 7499360008034, 32409295090379, 140526156635825, 610922936668375, 2662785799978942, 11636152939145004

Offset

0,3

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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A148837 A148838 A148839 * A047153 A281347 A000238

Adjacent sequences: A148837 A148838 A148839 * A148841 A148842 A148843

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved