Generalization of the Distance Fibonacci Sequences

被引：0
|
作者：
Yilmaz, Nur Seyma [1 ]
Wloch, Andrej [2 ]
Ozkan, Engin [3 ]
机构：
[1] Erzincan Binali Yildirim Univ, Grad Sch Nat & Appl Sci, TR-24100 Erzincan, Turkiye
[2] Rzeszow Univ Technol, Fac Math & Appl Phys, PL-35959 Rzeszow, Poland
[3] Marmara Univ, Fac Sci, Dept Math, TR-34722 Istanbul, Turkiye
来源：
AXIOMS | 2024年 / 13卷 / 07期
关键词：
distance Fibonacci numbers; generalized Fibonacci numbers; negative integers; matrix generators; HEISENBERG ALGEBRAS; NUMBERS;
D O I：
10.3390/axioms13070420
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this study, we introduced a generalization of distance Fibonacci sequences and investigate some of its basic properties. We then proposed a generalization of distance Fibonacci sequences for negative integers and investigated some basic properties. Additionally, we explored the construction of matrix generators for these sequences and offered a graphical representation to clarify their structure. Furthermore, we demonstrated how these generalizations can be applied to obtain the Padovan and Narayana sequences for specific parameter values.
引用
收藏
页数：16
相关论文
共 50 条
  • [1] ON A GENERALIZATION OF THE FIBONACCI SEQUENCE IN THE CASE OF 3 SEQUENCES
    ATANASSOV, KT
    FIBONACCI QUARTERLY, 1989, 27 (01): : 7 - 10
  • [2] New Identities for Generalized Fibonacci Sequences and New Generalization of Lucas Sequences
    Yayenie, Omer
    SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2012, 36 (05) : 739 - 752
  • [3] Generalized Fibonacci sequences and a generalization of the Q-matrix
    Zhang, ZZ
    FIBONACCI QUARTERLY, 1999, 37 (03): : 203 - 207
  • [4] Generalization of the 2-Fibonacci sequences and their Binet formula
    Ma, Timmy
    Vernon, Richard
    Arora, Gurdial
    NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2024, 30 (01) : 67 - 80
  • [5] Distance labelings: a generalization of Langford sequences
    Lopez, S. C.
    Muntaner-Batle, F. A.
    ARS MATHEMATICA CONTEMPORANEA, 2017, 12 (02) : 235 - 245
  • [6] Generalization of the Kummer identity and its application to Fibonacci-Lucas sequences
    Ma, XR
    FIBONACCI QUARTERLY, 1998, 36 (04): : 339 - 347
  • [7] A Generalization of a Fibonacci Identity
    Plaza, Angel
    Falcon, Sergio
    AMERICAN MATHEMATICAL MONTHLY, 2018, 125 (04): : 374 - 374
  • [8] ANOTHER FIBONACCI GENERALIZATION
    KLEITMAN, DJ
    AMERICAN MATHEMATICAL MONTHLY, 1991, 98 (10): : 958 - 959
  • [9] A Generalization of Fibonacci Groups
    V. G. Bardakov
    A. Yu. Vesnin
    Algebra and Logic, 2003, 42 (2) : 73 - 91
  • [10] GENERALIZATION OF FIBONACCI NUMBERS
    RECSKI, A
    FIBONACCI QUARTERLY, 1975, 13 (04): : 315 - 317
12345