  We introduce a sequence P_d of monic reciprocal polynomials with integer
coefficients having the central coefficients fixed as well as the peripheral
coefficients. We prove that the ratio between number of nonunimodular roots of
P_d and its degree d has a limit L when d tends to infinity. We show that if
the coefficients of a polynomial can be arbitrarily large in modulus then L can
be arbitrarily close to 0. It seems reasonable to believe that if the
coefficients are bounded then the analogue of Lehmer's Conjecture is true:
either L = 0 or there exists a gap so that L could not be arbitrarily close to
0. We present an algorithm for calculation the limit ratio and a numerical
method for its approximation. We estimated the limit ratio for a family of
polynomials. We calculated the limit ratio of polynomials correlated to many
bivariate polynomials having small Mahler measure.
