  Using $q$-trinomial coefficients of Andrews and Baxter along with the
technique of telescopic expansions, we propose and prove a complete set of
polynomial identities of Rogers-Ramanujan type for M(p, p+1) models of
conformal field theory perturbed by the operator $phi_{2,1}$. The bosonic form
of our polynomials is closely related to corner transfer matrix sums which
arise in the computation of the order parameter in the regime $1^+$ of
$A_{p-1}$ dilute models. In the limit where the degree of the polynomials tends
to infinity our identities provide new companion fermionic representations for
all Virasoro characters of unitary minimal series.
