Fibonacci–Pell hybridities

Abstract

We develop a recurrence satisfied by the Fibonacci and Pell families. We then use it to find explicit formulae and generating functions for the hybrids F n P n , L n P n , F n Q n and L n Q n , where F n , L n , P n and Q n denote the nth Fibonacci, Lucas, Pell and Pell-Lucas numbers, respectively. The recurrence enables us to find such relations for F 2 n , L 2 n , P 2 n and Q 2 n .