On Third-Order Bronze Fibonacci Numbers

Mücahit Akbiyik and Jeta Alo
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Mücahit Akbiyik: Department of Mathematics, Beykent University, Istanbul 34520, Turkey
Jeta Alo: Department of Mathematics, Beykent University, Istanbul 34520, Turkey

Mathematics, 2021, vol. 9, issue 20, 1-14

Abstract: In this study, we firstly obtain De Moivre-type identities for the second-order Bronze Fibonacci sequences. Next, we construct and define the third-order Bronze Fibonacci, third-order Bronze Lucas and modified third-order Bronze Fibonacci sequences. Then, we define the generalized third-order Bronze Fibonacci sequence and calculate the De Moivre-type identities for these sequences. Moreover, we find the generating functions, Binet’s formulas, Cassini’s identities and matrix representations of these sequences and examine some interesting identities related to the third-order Bronze Fibonacci sequences. Finally, we present an encryption and decryption application that uses our obtained results and we present an illustrative example.

Keywords: De Moivre-type identity; third-order Bronze Fibonacci numbers; Binet’s formula; Affine-Hill chipher (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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