A149710 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, 1), (1, -1, 0), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 71, 281, 1229, 5147, 22939, 99357, 447839, 1979645, 8996327, 40314685, 184327269, 834152475, 3832197717, 17470252835, 80572460719, 369423925933, 1709288794483, 7873100232727, 36528215139041, 168885181435067, 785423391146829, 3642764982035537, 16976349108943467, 78945960776413659

Offset

0,3

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + 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: A128887 A149708 A149709 * A149711 A149712 A017957

Adjacent sequences: A149707 A149708 A149709 * A149711 A149712 A149713

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved