A149674 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, 0, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 17, 65, 261, 1085, 4555, 19567, 84709, 370249, 1633547, 7258227, 32402035, 145428535, 655641593, 2966918443, 13471545253, 61360832927, 280227228003, 1282967187347, 5887316760711, 27071579408811, 124715117059779, 575561899922933, 2660508922424331, 12316490711071187, 57097128209758149

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, 1 + j, -1 + k, -1 + n] + aux[i, 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: A149673 A046231 A092896 * A149675 A149676 A149677

Adjacent sequences: A149671 A149672 A149673 * A149675 A149676 A149677

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved