A149896 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, 1), (0, 0, 1), (0, 1, 0), (1, 0, -1)}.

1, 2, 5, 14, 46, 160, 585, 2194, 8507, 33660, 135829, 555508, 2302992, 9648857, 40825201, 174125274, 748213686, 3235831779, 14076651319, 61555853379, 270458641654, 1193435185861, 5286972475995, 23505960789634, 104854537699871, 469163718426154, 2105190929074574, 9471098332799122

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, 1 + 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, 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: A240720 A232622 A149895 * A149897 A124527 A149898

Adjacent sequences: A149893 A149894 A149895 * A149897 A149898 A149899

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved