A151029 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, 0, 1), (0, 1, 0), (1, 0, 0)}.

1, 3, 9, 27, 87, 297, 1041, 3663, 13083, 47523, 174519, 642645, 2381481, 8893413, 33402909, 125690943, 474623079, 1800053415, 6850772907, 26107259823, 99713862171, 381909000663, 1466150482803, 5633995334529, 21683494576461, 83614271003217, 322964546792601, 1248391938849405, 4831066078825125

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

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[i, 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: A308520 A176826 A146786 * A179263 A147242 A148924

Adjacent sequences: A151026 A151027 A151028 * A151030 A151031 A151032

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved