• Title/Summary/Keyword: k-Fibonacci numbers

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SUM FORMULAE OF GENERALIZED FIBONACCI AND LUCAS NUMBERS

  • Cerin, Zvonko;Bitim, Bahar Demirturk;Keskin, Refik
    • Honam Mathematical Journal
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    • v.40 no.1
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    • pp.199-210
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    • 2018
  • In this paper we obtain some formulae for several sums of generalized Fibonacci numbers $U_n$ and generalized Lucas numbers $V_n$ and their dual forms $G_n$ and $H_n$ by using extensions of an interesting identity by A. R. Amini for Fibonacci numbers to these four kinds of generalizations and their first and second derivatives.

ON THE INTERSECTION OF k-FIBONACCI AND PELL NUMBERS

  • Bravo, Jhon J.;Gomez, Carlos A.;Herrera, Jose L.
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.2
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    • pp.535-547
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    • 2019
  • In this paper, by using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and $Peth{\ddot{o}}$, we find all generalized Fibonacci numbers which are Pell numbers. This paper continues a previous work that searched for Pell numbers in the Fibonacci sequence.

A Study on Teaching Material for Enhancing Mathematical Reasoning and Connections - Figurate numbers, Pascal's triangle, Fibonacci sequence - (수학적 추론과 연결성의 교수.학습을 위한 소재 연구 -도형수, 파스칼 삼각형, 피보나치 수열을 중심으로-)

  • Son, Hong-Chan
    • School Mathematics
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    • v.12 no.4
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    • pp.619-638
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    • 2010
  • In this paper, we listed and reviewed some properties on polygonal numbers, pyramidal numbers and Pascal's triangle, and Fibonacci sequence. We discussed that the properties of gnomonic numbers, polygonal numbers and pyramidal numbers are explained integratively by introducing the generalized k-dimensional pyramidal numbers. And we also discussed that the properties of those numbers and relationships among generalized k-dimensional pyramidal numbers, Pascal's triangle and Fibonacci sequence are suitable for teaching and learning of mathematical reasoning and connections.

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SINGULAR CASE OF GENERALIZED FIBONACCI AND LUCAS MATRICES

  • Miladinovic, Marko;Stanimirovic, Predrag
    • Journal of the Korean Mathematical Society
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    • v.48 no.1
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    • pp.33-48
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    • 2011
  • The notion of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,s)}$ of type s, whose nonzero elements are generalized Fibonacci numbers, is introduced in the paper [23]. Regular case s = 0 is investigated in [23]. In the present article we consider singular case s = -1. Pseudoinverse of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,-1)}$ is derived. Correlations between the matrix $\mathcal{F}_n^{(a,b,-1)}$ and the Pascal matrices are considered. Some combinatorial identities involving generalized Fibonacci numbers are derived. A class of test matrices for computing the Moore-Penrose inverse is presented in the last section.

FIBONACCI LENGTHS INVOLVING THE WALL NUMBER k(n)

  • DOOSTIE H.;HASHEMI M.
    • Journal of applied mathematics & informatics
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    • v.20 no.1_2
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    • pp.171-180
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    • 2006
  • Two infinite classes of special finite groups considered (The group G is special, if G' and Z(G) coincide). Using certain sequences of numbers we give explicit formulas for the Fibonacci lenghts of these classes which involve the well-known Wall numbers k(n).

ON A CLASS OF q-BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER RELATED TO SHELL-LIKE CURVES CONNECTED WITH THE FIBONACCI NUMBERS

  • Ahuja, Om P.;Cetinkaya, Asena;Bohra, Nisha
    • Honam Mathematical Journal
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    • v.42 no.2
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    • pp.319-330
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    • 2020
  • We introduce a new subclass of q-bi-univalent functions of complex order related to shell-like curves connected with the Fibonacci numbers. We obtain the coefficient estimates and Fekete-Szegö inequalities for the functions belonging to this class. Relevant connections with various other known classes have been illustrated.

CATALAN TRANSFORM OF THE κ-FIBONACCI SEQUENCE

  • Falcon, Sergio
    • Communications of the Korean Mathematical Society
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    • v.28 no.4
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    • pp.827-832
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    • 2013
  • In this paper we apply the Catalan transform to the ${\kappa}$-Fibonacci sequence finding different integer sequences, some of which are indexed in OEIS and others not. After we apply the Hankel transform to the Catalan transform of the ${\kappa}$-Fibonacci sequence and obtain an unusual property.

A NOTE ON THE MODIFIED k-FIBONACCI-LIKE SEQUENCE

  • Kwon, Youngwoo
    • Communications of the Korean Mathematical Society
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    • v.31 no.1
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    • pp.1-16
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    • 2016
  • The Fibonacci sequence is a sequence of numbers that has been studied for hundreds of years. In this paper, we introduce the modified k-Fibonacci-like sequence and prove Binet's formula for this sequence and then use it to introduce and prove the Catalan, Cassini, and d'Ocagne identities for the modified k-Fibonacci-like sequence. Also, the ordinary generating function of this sequence is stated.