Integers Represented by Binary Recursive Sequences

This paper is the continuation of Hajdu and Tijdeman (Ramanujan J 66:Article 74, 2025), where we deal with Lucas sequences. Here we study integers represented by integer sequences which satisfy binary recursive relations. In the case of non-degenerate sequences we give an upper bound on the largest index of a zero term and bounds on the growth order of the absolute values of the terms, both only in terms of the two initial values, which is a novel feature. Some of these bounds are best possible apart from a multiplicative constant.