A lattice path is a sequence of points 
, 
,
..., 
with 
such that each 
is a lattice point and
each difference 
belongs to a specified set of allowed steps. For unit horizontal
and vertical steps, 
is obtained by offsetting one unit east (or west) or one unit north (or south). Other
step sets may include diagonal steps (Rohatgi 1964, p. 470).
The number of paths of length 
from the origin (0,0) to a point
which are restricted to east and
north steps is given by the binomial coefficient 
for nonnegative
integers 
and 
.
