Some Properties of Generalized Third Order Pell Numbers

This paper considers some properties of the third order recursive sequence defined by the linear recurrence relation , 2 , 1 , 0 , 3 , 2 3 , 2 , , = ≥ + = − − m n w w w n m n m m n m , with appropriate initial conditions. The present work follows on from the case m = 0 (Shannon et al). Relationships with the well-known sequences of Fibonacci, Lucas and Pell are developed. The motivation for the study was to find analogous results to some of the second order classic identities such as, for example, Simson’s identity and Horadam’s Fibonacci number triples.