On a generalization for Fibonacci quaternions

Abstract

In this study, we introduced a quaternion sequence which has not been introduced before. We show that the new quaternion sequence that we introduced includes the previously introduced Fibonacci, Lucas, Pell, Pell–Lucas, Jacobsthal and Jacobsthal–Lucas quaternion sequences. We obtained the Binet formula and calculated the Cassini identity, summation formula and the norm value for this new quaternion sequence.