New proofs of linear recurrence identities for terms of the Horadam sequence.

Abstract

We state, and prove using matrices, two (related) linear recurrence identities for termsofthesocalledHoradamsequence;eachresultexpressesthegeneraltermofthesequence as a linear combination of terms with particular initial values. First offered by A.F. Horadam himself in the 1960s, our approach to their formulation is quite different and, we believe, new.