A148762 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, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 3, 7, 29, 79, 341, 1067, 4745, 15959, 72573, 256539, 1183001, 4339855, 20218213, 76289395, 358226465, 1382092567, 6530138429, 25653670427, 121817296793, 485782664255, 2316312416629, 9354426554179, 44758972207377, 182723834863591, 876884290189229, 3613464410162539, 17385130330867977

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A148760 A148761 A186732 * A096064 A148763 A148764

Adjacent sequences: A148759 A148760 A148761 * A148763 A148764 A148765

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved