General information on vector valued groupoids and $(n,m)$-operations can be found in [1]. In this paper we define and consider (1,2)-sequences, which are related to (1,2)-operations. By using these (1,2)—sequences we give a combinatorial proof of a problem posed in [2] (different to that given in [1]) that every free (1,2)-groupoid is a proper (1,2)-subsemigroup of a semigroup. Several combinatorial properties of (1,2)-sequences are also obtained.