Coloring link diagrams and Conway-type polynomial of braids

In this paper we define and present a simple combinatorial formula for a 3-variable Laurent polynomial invariant I(a,z,t) of conjugacy classes in Artin braid group Bm. We show that the Laurent polynomial I(a,z,t) satisfies the Conway skein relation and the coefficients of the 1-variable polynomial t−kI(a,z,t)|a=1,t=0 are Vassiliev invariants of braids.