  Turning the skein relation for HOMFLY into a Fibonacci recurrence, we prove
that there are only three rational specializations of HOMFLY polynomial:
Alexander-Conway, Jones, and a new one. Using the recurrence relation, we find
general and relative expansion formulae and rational generating functions for
Alexander-Conway polynomial and the new polynomial, which reduce the
computations to closure of simple braids, a subset of square free braids;
HOMFLY polynomials of these simple braids are also computed. Algebraic
independence of these three polynomials is proved.
