A NON-LINEAR RECURRENCE IDENTITY CLASS FOR TERMS OF A GENERALIZED LINEAR RECURRENCE SEQUENCE OF DEGREE THREE

摘要

We state, and prove by a succinct matrix method, a new non-linear identity for terms generated by a general (linear) third order recurrence equation, and show it recovers a result for the well-known Horadam sequence. We then produce a fully generalized version of the identity that possesses three additional characterizing parameters and describes a new class of identities.