This study considers the m−order linear recursive sequences yielding some well-known
sequences (such as the Fibonacci, Lucas, Pell, Jacobsthal, Padovan, and Perrin sequences). Also,
the Binet-like formulas and generating functions of the m−order linear recursive sequences have
been derived. Then, we define the m−order linear recursive quaternions, and give the Binet-like
formulas and generating functions for them.