A151104 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, 1, 0)}

1, 3, 11, 43, 187, 815, 3757, 17183, 81465, 382501, 1842955, 8795475, 42805051, 206505321, 1011728125, 4917939433, 24206397975, 118314241575, 584299089711, 2867687531201, 14197274934419, 69899884033057, 346708095725505, 1711247426205119, 8500195491944077, 42037434056718197, 209047588568217113

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, 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: A049163 A049180 A049152 * A138787 A110052 A300626

Adjacent sequences: A151101 A151102 A151103 * A151105 A151106 A151107

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved