On the sequence related to Lucas numbersand its properties

Cassini’s, Catalan’s, d’Ocagne’s, etc. using matrix algebra. Moreover, an extended Binet’s formula for {Lk,n} and, thereby, identities such as k = 1. Modified Pell-Lucas sequence is {Lk,n} with k = 2. We produce generalization. The Lucas sequence is a special case of {Lk,n} with is integer number. Some well-known sequence are special case of this k,n k,n−1 k,n−the recurrence relation L = kL + L 2 for n  2, where k with initial conditions Lk,0 = 2 and Lk,1 = 1, which is generated by rence relation. In this article, we study a new generalization {Lk,n}, by preserving the initial conditions, and others by preserving the recur- The Fibonacci sequence has been generalized in many ways, somewe present sum formulas concerning this new generalization.