On a generalization for fibonacci quaternions

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.