A note on a transform to self-inverse sequences

Abstract

The sequences which are fixed by the binomial transform are called self-inverse sequences. In this paper, an identity satisfied by Fibonacci numbers is modified to provide a transform which maps a specific subset of sequences to self-inverse sequences bijectively. The image of some classes of sequences under this transform are explicitly found which provides a new formulation and a class of examples of self-inverse sequences. A criterion for the solutions of some difference equations to be self-inverse is also given.