In this paper, we present a generalization of well-known k-Fibonacci sequence. Namely, defined generalized This sequence generalizes others, sequence, classical Fibonacci Pell and Jacobsthal We establish some the interesting properties Also, obtain generating function for them.

In this paper we consider the generalized order-k Fibonacci and Lucas numbers. We give the generalized Binet formula, combinatorial representation and some relations involving the generalized order-k Fibonacci and Lucas numbers.