A149863 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), (1, 0, 0), (1, 0, 1)}.

1, 2, 5, 13, 40, 123, 412, 1341, 4746, 16272, 58855, 206111, 763450, 2740091, 10250705, 37195701, 140952500, 518767740, 1976234997, 7321175439, 28112193490, 105105989815, 404852222574, 1520206042888, 5886807485023, 22247026512023, 86320820151357, 327211300970772, 1274413096031914, 4853723781334134

Offset

0,2

Links

Table of n, a(n) for n=0..29.

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, -1 + k, -1 + n] + aux[-1 + i, j, 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: A287967 A133448 A149862 * A371714 A291614 A202153

Adjacent sequences: A149860 A149861 A149862 * A149864 A149865 A149866

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved