Properties and applications of some special integer number sequences

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.

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Properties and applications of some special integer number sequences

Abstract: In this paper, we provide properties and applications of some special integer sequences. We generalize and give some properties of Pisano period. Moreover, we provide a new application in Cryptography and applications of some quaternion elements.

Cited by 2 publications

References 17 publications

Some diagonalizable matrices, connected with difference equations of degree 3

Some diagonalizable matrices, connected with difference equations of degree 3

On Third-Order Bronze Fibonacci Numbers

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