… well known Lucas sequence and second one is the Pell-Lucas sequence. For this reason,
we have decided to call them The k-Lucas Sequences. Elements of these sequences, say Lk …

… In this paper, we address a similar problem in the family of k-Lucas sequences. We also show
that the k-Lucas sequences have similar properties to those of k-Fibonacci sequences and …

… Also, Deveci et al. obtained the periods of the k-nacci sequences … sequences of the generalized
order-k Lucas numbers and we examine the periods of the ith generalized order-k Lucas …

… In this subsection, we recall some facts and properties of the k-generalized Lucas
sequence which will be used later. It is known that the characteristic polynomial of the k-generalized …

… sequence (Fn)n≥0. On the other hand, if a = 2 and b = 1, then G(k) is known as the k−Lucas
sequence L(… case of k = 2, we obtain the usual Lucas companion of the Fibonacci sequence …

… We now introduce k-Lucas sequences. We let Ln represent the nth Lucas number, that is, for
n ⩾ 1, Ln = Fn−1 + Fn+1, where F0 … We call l(k) n the nth k-Lucas number. Then we have l(k) …

… k-Lucas numbers, and then for the even and the odd k-Lucas … k-Lucas numbers. Then,
we prove a relation between the k-Fibonacci numbers of indexes of the form 2rn and the k-Lucas …

… and the k-Lucas numbers and we remember some of the properties that … or k-Lucas numbers
with subscripts in linear form and … Fibonacci and the k-Lucas numbers is based on the same …

… of Lucas sequence, which is called the k-Lucas sequence for … In this paper, we give a
representation of nth k-Lucas numbers … k-Lucas number In [1], the author gave two matrices S(k) …

The Fibonacci sequence is a sequence of numbers that has been studied for hundreds of
years. In this paper, we introduce the new sequence S_{k,n} with initial conditions S_{k,0} = 2b …