  We describe rational knots with any of the possible combinations of the
properties (a)chirality, (non-)positivity, (non-)fiberedness, and unknotting
number one (or higher), and determine exactly their number for a given number
of crossings in terms of their generating functions. We show in particular how
Fibonacci numbers occur in the enumeration of fibered achiral and unknotting
number one rational knots. Then we show how to enumerate rational knots by
crossing number and genus and/or signature. This allows to determine the
distribution of these invariants among rational knots. We give also an
application to the enumeration of lens spaces.
