On the Number of Exceptional Pairs Over a Class of Nakayama Algebras

In this paper some combinatorial and homological tools are used to describe and give an explicit formula for the number of exceptional pairs (exceptional sequences of length two) for some classes of Nakayama Algebras and for the Auslander algebra of a radical square zero algebra of type ${\mathbb{A}}_n$. In addition, we explore how the number of exceptional pairs can be connected with some integer sequences in the OEIS (The On-line Encyclopedia of Integer Sequences).