On some multiple zeta-star values of one-two-three indices

In this paper, we present some identities for multiple zeta-star values with indices obtained by inserting 3 or 1 into the string 2,…,2. Our identities give analogues of Zagier’s evaluation of \zeta(2,…,2,3,2,…, 2) and examples of a kind of duality of multiple zeta-star values. Moreover, their generalizations give partial solutions of conjectures proposed by Imatomi, Tanaka, Wakabayashi and the first author.