On k-Lucas sequences

For positive integers n and k, the k-Lucas sequence is defined by the recurrence relation L_{n+1= kL n}+L_n-1 with the initial values L₀ = 2, L₁ = k. The Lucas sequence and Pell-Lucas sequence are two special cases of the k-Lucas sequence. Using a matrix approach, we uncover some new facts concerning the k-Lucas sequence.