  The incomplete tribonacci polynomials, denoted by T_n^{(s)}(x), generalize
the usual tribonacci polynomials T_n(x) and were introduced in [10], where
several algebraic identities were shown. In this paper, we provide a
combinatorial interpretation for T_n^{(s)}(x) in terms of weighted linear
tilings involving three types of tiles. This allows one not only to supply
combinatorial proofs of the identities for T_n^{(s)}(x) appearing in [10] but
also to derive additional identities. In the final section, we provide a
formula for the ordinary generating function of the sequence T_n^{(s)}(x) for a
fixed s, which was requested in [10]. Our derivation is combinatorial in nature
and makes use of an identity relating T_n^{(s)}(x) to T_n(x).
