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On a generalization of duality triads

Matthias Schork (2006)

Open Mathematics

Some aspects of duality triads introduced recently are discussed. In particular, the general solution for the triad polynomials is given. Furthermore, a generalization of the notion of duality triad is proposed and some simple properties of these generalized duality triads are derived.

On a generalization of the Pell sequence

Jhon J. Bravo, Jose L. Herrera, Florian Luca (2021)

Mathematica Bohemica

The Pell sequence ( P n ) n = 0 is the second order linear recurrence defined by P n = 2 P n - 1 + P n - 2 with initial conditions P 0 = 0 and P 1 = 1 . In this paper, we investigate a generalization of the Pell sequence called the k -generalized Pell sequence which is generated by a recurrence relation of a higher order. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences. Some interesting identities involving the Fibonacci and generalized Pell numbers are also deduced....

On Balancing and Lucas-balancing Quaternions

Bijan Kumar Patel, Prasanta Kumar Ray (2021)

Communications in Mathematics

The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas, summation formulas, Catalan's identity, etc. concerning these quaternions are also established.

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