In this paper, we give some determinantal and permanental representations of generalized bivariate Lucas p-polynomials by using various Hessenberg matrices. The results that we obtained are important since generalized bivariate Lucas p-polynomials are general forms of, for example, bivariate Jacobsthal-Lucas, bivariate Pell-Lucas ppolynomials, Chebyshev polynomials of the first kind, Jacobsthal...

In this work, we investigate the hyperbolic k-Jacobsthal and k-Jacobsthal–Lucas octonions. We give Binet’s Formula, Cassini’s identity, Catalan’s d’Ocagne generating functions of Also, present many properties these

We introduce a function on sequences, which we call the Pfaffian transform, using the Pfaffian of a skew-symmetric matrix. We establish several basic properties of the Pfaffian transform, and we use the transfer matrix method to show that the set of sequences with rational generating functions is closed under the Pfaffian transform. We conclude by computing the Pfaffian transform of a variety o...

Let {ai,j} be real numbers for 0 6 i 6 r 1 and 1 6 j 6 2, and define a sequence {vn} with initial conditions v0, v1 and conditional linear recurrence relation vn = at,1vn 1 + at,2vn 2 where n ⌘ t (mod r) (n > 2). The sequence {vn} can be viewed as a generalization of many well-known integer sequences, such as Fibonacci, Lucas, Pell, Jacobsthal, etc. We find explicitly a linear recurrence equati...

Horadam [7], in a recent article, defined two sequences of polynomials Jn(x) and j„(x), the Jacobsthal and Jacobsthal-Lucas polynomials, respectively, and studied their properties. In the same article, he also defined and studied the properties of the rising and descending polynomials i^(x), rn(x), Dn(x)y and dn(x), which are fashioned in a manner similar to those for Chebyshev, Fermat, and oth...