Some Binomial Sums of k-Pell, k-Pell-Lucas and Modified k-Pell Numbers

The main goal of this paper is to find some new identities containing k-Pell and k-Pell-Lucas numbers. In addition, we use these identities to prove binomial properties of k-Pell, k-Pell-Lucas, and modified k-Pell numbers. It is possible to prove some new properties of k-Pell, k-Pell-Lucas and modified k-Pell numbers based on the obtained results. The generated functions can also be expressed in closed form using them.