IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v153y2021ip2s0960077921008766.html
   My bibliography  Save this article

On the co-complex-type k-Fibonacci numbers

Author

Listed:
  • Deveci, Ömür
  • Hulku, Sakine
  • Shannon, Anthony G.

Abstract

In this paper, we define the co-complex-type k-Fibonacci numbers and then give the relationships between the k-step Fibonacci numbers and the co-complex-type k-Fibonacci numbers. Also, we produce various properties of the co-complex-type k-Fibonacci numbers such as the generating matrices, the Binet formulas, the combinatorial, permanental and determinantal representations, and the finite sums by matrix methods. In addition, we study the co-complex-type k-Fibonacci sequence modulo m and then we give some results concerning the periods and the ranks of the co-complex-type k-Fibonacci sequences for any k and m. Furthermore, we extend the co-complex-type k-Fibonacci sequences to groups. Finally, we obtain the periods of the co-complex-type 2-Fibonacci sequences in the semidihedral group SD2m, (m≥4) with respect to the generating pair (x,y).

Suggested Citation

  • Deveci, Ömür & Hulku, Sakine & Shannon, Anthony G., 2021. "On the co-complex-type k-Fibonacci numbers," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008766
    DOI: 10.1016/j.chaos.2021.111522
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921008766
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111522?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Stakhov, Alexey & Rozin, Boris, 2006. "The continuous functions for the Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1014-1025.
    2. Falcon, Sergio & Plaza, Ángel, 2009. "k-Fibonacci sequences modulo m," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 497-504.
    3. Stakhov, Alexey & Rozin, Boris, 2006. "Theory of Binet formulas for Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1162-1177.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
    2. Kocer, E. Gokcen & Tuglu, Naim & Stakhov, Alexey, 2009. "On the m-extension of the Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1890-1906.
    3. Kılıç, Emrah, 2009. "The generalized Pell (p,i)-numbers and their Binet formulas, combinatorial representations, sums," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2047-2063.
    4. Hatir, E. & Noiri, T., 2009. "On δ–β-continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 205-211.
    5. Stakhov, Alexey, 2007. "The generalized golden proportions, a new theory of real numbers, and ternary mirror-symmetrical arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 315-334.
    6. Büyükkılıç, F. & Demirhan, D., 2009. "Cumulative growth with fibonacci approach, golden section and physics," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 24-32.
    7. Anatriello, Giuseppina & Németh, László & Vincenzi, Giovanni, 2022. "Generalized Pascal’s triangles and associated k-Padovan-like sequences," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 278-290.
    8. Falcón, Sergio & Plaza, Ángel, 2009. "On k-Fibonacci sequences and polynomials and their derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1005-1019.
    9. Ekici, Erdal & Noiri, Takashi, 2009. "Decompositions of continuity, α-continuity and AB-continuity," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2055-2061.
    10. E. Gokcen Kocer & Huriye Alsan, 2022. "Generalized Hybrid Fibonacci and Lucas p-numbers," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 948-955, December.
    11. Esmaeili, Morteza & Esmaeili, Mostafa, 2009. "Polynomial Fibonacci–Hessenberg matrices," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2820-2827.
    12. Stakhov, A.P., 2007. "The “golden” matrices and a new kind of cryptography," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1138-1146.
    13. Ekici, Erdal, 2009. "A note on almost β-continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1010-1013.
    14. Ekici, Erdal, 2008. "Generalization of weakly clopen and strongly θ-b-continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 79-88.
    15. Fiorenza, Alberto & Vincenzi, Giovanni, 2011. "Limit of ratio of consecutive terms for general order-k linear homogeneous recurrences with constant coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 145-152.
    16. Stakhov, Alexey & Rozin, Boris, 2007. "The “golden” hyperbolic models of Universe," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 159-171.
    17. Falcón, Sergio & Plaza, Ángel, 2008. "On the 3-dimensional k-Fibonacci spirals," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 993-1003.
    18. Flavio Pressacco & Giacomo Plazzotta & Laura Ziani, 2014. "K-Fibonacci sequences and minimal winning quota in Parsimonious game," Working Papers hal-00950090, HAL.
    19. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    20. Nalli, Ayse & Haukkanen, Pentti, 2009. "On generalized Fibonacci and Lucas polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3179-3186.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008766. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.