Complex Narayana Quaternions

Abstract

Here, we first introduce complex Narayana numbers. Then, we describe a new quaternion sequence whose coefficients consist of complex Narayana numbers and that we named with complex Narayana quaternions. We also give the generating function, exponential generating function, Binet formula, and summation formulas for these sequences. Finally, we obtain a matrix representation of complex Narayana quaternions and make an application related to the matrix representation of complex Narayana quaternions.