A149660 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, 0), (0, 1, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 59, 239, 995, 3999, 16717, 72381, 310285, 1336973, 5875781, 25978769, 114569141, 509761121, 2285807767, 10256654727, 46123726015, 208655609019, 946466452167, 4297155238315, 19570660154959, 89412110702627, 409003296517919, 1873831511833471, 8605870285350615, 39588128811366087

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[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A149657 A149658 A149659 * A149661 A146130 A026619

Adjacent sequences: A149657 A149658 A149659 * A149661 A149662 A149663

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved