The Stern poset S is a graded infinite naturally associated with Stern's triangle, which was defined by Stanley, in analogy Pascal's triangle. Stanley noted that every interval distributive lattice. Let Pn denote the unique (up to isomorphism) for set of its order ideals, ordered inclusion, isomorphic from element row 0 triangle n-th r sufficiently large r. For n?1 letLn(q)=2?(?k=12n?1APk(q))+A...