  A new direct method of obtaining reductions of the Toda equation is
described. We find a canonical and complete class of all possible reductions
under certain assumptions. The resulting equations are ordinary
differential-difference equations, sometimes referred to as delay-differential
equations. The representative equation of this class is hypothesized to be a
new version of one of the classical Painlev\'e equations. The Lax pair
associated to this equation is obtained, also by reduction.

Exactly Solvable and Integrable Systems