This book presents the state-of-the-art results concerning recurrent sequences and their
practical applications in algebra, number theory, geometry of the complex plane, discrete …

Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions Page 1 DOI:
10.1515/auom-2015-0037 An. St. Univ. Ovidius Constanta Vol. 23(2),2015, 201–212 Some …

In this study, we introduced a quaternion sequence which has not been introduced before.
We show that the new quaternion sequence that we introduced includes the previously …

This paper connects two attractive topics in applied mathematics, r-circulant matrices and
the Chebyshev polynomials. The r-circulant matrices whose entries are the Chebyshev …

This paper takes a historical view of some long-standing problems associated with the
development of sums of Fibonacci numbers in which the latter have powers of integers as …

In this study, we introduce a new classes of quaternion numbers. We show that this new
classes quaternion numbers include all of quaternion numbers such as Fibonacci, Lucas …

Horadam sequences are second-order linear recurrence sequences which depend on a
family of four parameters (two in the defining recursion itself, and two initial values). In this …

We give an update on work relating to Horadam sequences that are generated by a general
linear recurrence formula of order two. This article extends a first ever survey published in …

In this paper, we firstly introduce k− Fibonacci and k− Lucas hybrid numbers and then give
some of their algebraic properties. Additionally, we investigate the Binet formulas, the …

Some special families of finite sums with squared Horadam numbers and generalized
tribonacci numbers are discussed. As special cases of our results sums with squared …