Generalized k-Pell and k-Pell Lucas sequences and their matrix representations

In this study, k-Pell, k-Pell Lucas and Modified k-Pell sequences are considered. In the first section, the basic identities between Pell, Pell Lucas and Modified Pell sequences are discussed by means of their recurrence relations. In the second section, several studies about k-Pell, k-Pell Lucas and Modified k-Pell sequences are considered. In the third section, the matrix representations of these sequences are presented. The generalized k-Pell, k-Pell Lucas ve Modified k-Pell sequences are given with their recurrence relations and matrix ways in the fourth section. In the fifth section, the generalized k-Pell and k-Pell Lucas sequences are given with the appropriate initial conditions and afterwards, order k-Pell and order k-Pell Lucas sequences are defined by using matrix representations corresponding them. Last section involves some discussions and suggestions about the study.