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From Fibonacci Sequence to More Recent Generalisations

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Mathematical Methods for Engineering Applications (ICMASE 2021)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 384))

Abstract

Number sequences have been the subject of several research studies. From the algebraic properties to the generating matrices and generating functions of these sequences, all these topics and many others have been studied by several researchers and a vast bibliography covers this type of sequences. When in 2013 the first author had an initial contact with this topic, she soon turned to other sequences of numbers and began a careful investigation with great enthusiasm. A group of researchers interested in these themes was formed, based on the most recent works on this subject of number sequences, they developed new generalisations of some of them, introducing the respective definitions, properties and some results concerning those sequences. In this paper we propose a tour of our work involving the number sequences we have been studying over the past eight years, either jointly or individually.

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Acknowledgements

The first author is member of the Research Centre CMAT-UTAD and also a collaborating member of the Research Centre CIDTFF. The second author is member of the Research Centre CIDTFF. This research was partially financed by Portuguese Funds through FCT -Fundação para a Ciência e a Tecnologia, within the Projects UIDB/00013/2020, UIDP/00013/2020 and UIDB/00194/2020.

Author information

Authors and Affiliations

  1. Department of Mathematics, School of Science and Technology, University of Trás-os-Montes e Alto Douro, Vila Real, Portugal

    Paula Catarino & Helena Campos

  2. Research Centre of Mathematics, University of Minho-Polo CMAT-UTAD, Vila Real, Portugal

    Paula Catarino

Authors
  1. Paula Catarino
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  2. Helena Campos
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Corresponding authors

Correspondence to Paula Catarino or Helena Campos .

Editor information

Editors and Affiliations

  1. Faculty of Arts and Sciences, Ankara Hacı Bayram Veli University, Ankara, Turkey

    Fatih Yilmaz

  2. Institute of Fundamental Physics and Mathematics, University of Salamanca, Salamanca, Spain

    Araceli Queiruga-Dios

  3. Faculty of Sciences, University of Salamanca, Salamanca, Spain

    María Jesús Santos Sánchez

  4. Polytechnic Institute of Coimbra (ISEC), Coimbra, Portugal

    Deolinda Rasteiro

  5. Institute of Physical and Information Technologies (ITEFI), Spanish National Research Council (CSIC), Madrid, Spain

    Víctor Gayoso Martínez

  6. Institute of Fundamental Physics and Mathematics, University of Salamanca, Salamanca, Spain

    Jesús Martín Vaquero

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Catarino, P., Campos, H. (2022). From Fibonacci Sequence to More Recent Generalisations. In: Yilmaz, F., Queiruga-Dios, A., Santos Sánchez, M.J., Rasteiro, D., Gayoso Martínez, V., Martín Vaquero, J. (eds) Mathematical Methods for Engineering Applications. ICMASE 2021. Springer Proceedings in Mathematics & Statistics, vol 384. Springer, Cham. https://doi.org/10.1007/978-3-030-96401-6_24

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