A149975 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, 1, 1), (0, 0, -1), (0, 1, 0), (1, 0, 0)}.

1, 2, 5, 16, 56, 205, 782, 3087, 12476, 51334, 214466, 907747, 3883324, 16763121, 72929623, 319477994, 1407947296, 6237863865, 27767667839, 124133911734, 557062608329, 2508555008669, 11332172067194, 51340002679377, 233210054081100, 1061930828847765, 4846423371871309, 22164143028120382

Offset

0,2

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, 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] + 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: A052708 A149973 A149974 * A149976 A141201 A149977

Adjacent sequences: A149972 A149973 A149974 * A149976 A149977 A149978

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved