  HOMFLY polynomials are one of the major knot invariants being actively
studied. They are difficult to compute in the general case but can be far more
easily expressed in certain specific cases. In this paper, we examine two
particular knots, as well as one more general infinite class of knots. From our
calculations, we see some apparent patterns in the polynomials for the knots
$9_{35}$ and $9_{46}$, and in particular their $F$-factors. These properties
are of a form that seems conducive to finding a general formula for them, which
would yield a general formula for the HOMFLY polynomials of the two knots.
Motivated by these observations, we demonstrate and conjecture some properties
both of the $F$-factors and HOMFLY polynomials of these knots and of the more
general class that contains them, namely pretzel knots with 3 odd parameters.
We make the first steps toward a matrix-less general formula for the HOMFLY
polynomials of these knots.
