Skip to main content
SpringerLink
Log in

Generalizations of the Fibonacci Sequence with Zig-Zag Walks

  • Conference paper
  • First Online:
Mathematics and Computation (IACMC 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 418))

Included in the following conference series:

  • 234 Accesses

Abstract

The examination of the recurrence sequences associated with combinatorial constructions has been very extensive in the last decades. One of the most famous recurrence sequences is the Fibonacci sequence. We give two digraph constructions defined on the hyperbolic and on the Euclidean square mosaics, respectively, and we introduce two zig-zag type walks associating to the Fibonacci and its generalized sequences. Then we determine the recurrence relations and we give some examples.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Belbachir, H., Németh, L., Szalay, l.: Hyperbolic Pascal triangles. Appl. Math. Comput. 273, 453–464 (2016). https://doi.org/10.1016/j.amc.2015.10.001

  2. Németh, L., Szalay, L.: Recurrence sequences in the hyperbolic Pascal triangle corresponding to the regular mosaic \(\{4,5\}\). Ann. Math. Inform. 46, 165–173 (2016)

    MathSciNet  MATH  Google Scholar 

  3. Németh, L., Szalay, L.: Sequences involving square zig-zag shapes. J. Integer Seq. 24(5), Article 21.5.2 (2021)

    Google Scholar 

  4. Sloane, N.J.A., et al.: The on-line encyclopedia of integer sequences, (2021). https://oeis.org/

Download references

Author information

Authors and Affiliations

  1. University of Sopron, Sopron, 9400, Bajcsy Zs. u. 4, Hungary

    László Németh & László Szalay

  2. University J. Selye, 945 01, Hradná str. 21, Komárno, Slovakia

    László Szalay

Authors
  1. László Németh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. László Szalay
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to László Németh .

Editor information

Editors and Affiliations

  1. School of Basic Sciences and Humanities, German Jordanian University, Amman, Jordan

    Dia Zeidan

  2. Department of Applied Mathematics, Universitat Politècnica de València, Valencia, Spain

    Juan C. Cortés

  3. Department of Mathematics, Zarqa University, Zarqa, Jordan

    Aliaa Burqan

  4. Department of Mathematics, Zarqa University, Zarqa, Jordan

    Ahmad Qazza

  5. MNZ, Leipzig University of Applied Sciences, Leipzig, Germany

    Jochen Merker

  6. Department of Mathematics, Zarqa University, Zarqa, Jordan

    Gharib Gharib

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Németh, L., Szalay, L. (2023). Generalizations of the Fibonacci Sequence with Zig-Zag Walks. In: Zeidan, D., Cortés, J.C., Burqan, A., Qazza, A., Merker, J., Gharib, G. (eds) Mathematics and Computation. IACMC 2022. Springer Proceedings in Mathematics & Statistics, vol 418. Springer, Singapore. https://doi.org/10.1007/978-981-99-0447-1_26

Download citation

Publish with us

Policies and ethics

Search

Navigation