A149659 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, 1, 0), (0, 0, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 59, 239, 995, 3967, 16765, 72109, 309069, 1335741, 5867669, 25895073, 114438661, 509003953, 2281926919, 10241361527, 46062876287, 208403698167, 945304439507, 4291646557315, 19550896097955, 89320268757243, 408547143010603, 1872035048129199, 8597931395864235, 39550378044489787

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A287804 A149657 A149658 * A149660 A149661 A146130

Adjacent sequences: A149656 A149657 A149658 * A149660 A149661 A149662

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved