A148853 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, 1, 1), (1, -1, -1), (1, 1, -1)}.

1, 1, 3, 8, 28, 91, 352, 1306, 5182, 20797, 85424, 355119, 1504967, 6418859, 27758070, 120917363, 531015804, 2349303542, 10455790760, 46802437636, 210614263933, 951984893677, 4322352594813, 19700431190212, 90116118871500, 413622990248458, 1904276004073268, 8792668328752535, 40707759528449518

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, -1 + 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: A148850 A148851 A148852 * A148854 A148855 A148856

Adjacent sequences: A148850 A148851 A148852 * A148854 A148855 A148856

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved