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Applicable Algebra in Engineering, Communication and Computing

05-11-2024 | Original Paper

The complex-type k-Padovan sequences and their applications

Authors: Ömür Deveci, Anthony G. Shannon, Özgür Erdağ, Güntaç Ceco

Published in: Applicable Algebra in Engineering, Communication and Computing

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Abstract

In this paper, we define the complex-type k-Padovan numbers and then give the relationships between the \(\left( 1,k-1\right)\)-bonacci numbers, the k -Padovan numbers and the complex-type k-Padovan numbers by matrix method. In addition, we study the complex-type k-Padovan sequence modulo m and then we show that for some m the periods of the complex type k-Padovan and k-Padovan sequences modulo m are related. Furthermore, we extend the complex-type k-Padovan sequences to groups. Finally, we obtain the periods of the complex-type 4, 5, 6-Padovan sequences in the semidihedral group \(SD_{2^{m}}\), \(\left( m\ge 4\right)\) with respect to the generating pairs \(\left( x,y\right)\) and \(\left( y,x\right)\).

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Metadata
Title
The complex-type k-Padovan sequences and their applications
Authors
Ömür Deveci
Anthony G. Shannon
Özgür Erdağ
Güntaç Ceco
Publication date
05-11-2024
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-024-00672-4

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