Displaying similar documents to “On Balancing and Lucas-balancing Quaternions”

Gelin-Cesáro identities for Fibonacci and Lucas quaternions

Ahmet Daşdemir (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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To date, many identities of different quaternions, including the Fibonacci and Lucas quaternions, have been investigated. In this study, we present Gelin-Cesáro identities for Fibonacci and Lucas quaternions. The identities are a worthy addition to the literature. Moreover, we give Catalan's identity for the Lucas quaternions.

An inequality for Fibonacci numbers

Horst Alzer, Florian Luca (2022)

Mathematica Bohemica

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We extend an inequality for Fibonacci numbers published by P. G. Popescu and J. L. Díaz-Barrero in 2006.

Binomials transformation formulae for scaled Fibonacci numbers

Edyta Hetmaniok, Bożena Piątek, Roman Wituła (2017)

Open Mathematics

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The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.

The positivity problem for fourth order linear recurrence sequences is decidable

Pinthira Tangsupphathawat, Narong Punnim, Vichian Laohakosol (2012)

Colloquium Mathematicae

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The problem whether each element of a sequence satisfying a fourth order linear recurrence with integer coefficients is nonnegative, referred to as the Positivity Problem for fourth order linear recurrence sequence, is shown to be decidable.