A STUDY ON THE SUMS OF SQUARES OF GENERALIZED TRIBONACCI NUMBERS: CLOSED FORM FORMULAS OF ∑_{k=0}ⁿkx^{k}W_{k}² [PDF]
, 2021 In this paper, closed forms of the sum formulas ∑_{k=0}ⁿkx^{k}W_{k}², ∑_{k=0}ⁿkx^{k}W_{k+2}W_{k} and ∑_{k=0ⁿkx^{k}W_{k+1}W_{k} for the squares of generalized Tribonacci numbers are presented.
Yüksel SOYKAN, SOYKAN, Yüksel
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Here we find the Padovan and Perrin numbers that are concatenations of two terms of the other sequence. We also find the intersection between these ternary sequences. [PDF]
, 2023 Here we find the Padovan and Perrin numbers that are concatenations of two terms of the other sequence. We also find the intersection between these ternary sequences.
Bravo, Eric Fernando
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On the solutions of two special types of Riccati difference equation via Fibonacci numbers [PDF]
, 2013 In this study, we investigate the solutions of two special types of the Riccati difference equation and such that their solutions are associated with Fibonacci numbers.
Necati Taskara +5 more
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Diophantine triples in a Lucas-Lehmer sequence [PDF]
, 2018 In this paper, we define a Lucas-Lehmer type sequence denoted by (Ln)1n=0, and show that there are no integers 0 < a < b < c such that ab + 1, ac + 1 and bc + 1 all are terms of the sequence. Keywords: Diophantine triples, Lucas-Lehmer sequences MSC:
Gueth, Krisztián
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On identities with multinomial coefficients for Fibonacci-Narayana sequence [PDF]
, 2018 In this paper we study some families of Toeplitz-Hessenberg determinants the entries of which are Fibonacci-Narayana (or Narayana’s cows) numbers. This leads to discover some identities for these numbers. In particular, we establish connection between
Goy, Taras
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Extended Fibonacci numbers and polynomials with probability applications
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 50, Page 2681-2693, 2004., 2004 The extended Fibonacci sequence of numbers and polynomials is introduced and studied. The generating function, recurrence relations, an expansion in terms of multinomial coefficients, and several properties of the extended Fibonacci numbers and polynomials are obtained.
Demetrios L. Antzoulakos
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 39, Page 2507-2518, 2003., 2003 We prove that powers of 4‐netted matrices (the entries satisfy a four‐term recurrence δai,j = αai−1,j + βai−1,j + γai,j−1) preserve the property of nettedness: the entries of the eth power satisfy δeai,j(e)=αeai−1,j(e)+βeai−11,j−(e)+γeai,j−1(e), where the coefficients are all instances of the same sequence xe+1 = (β + δ)xe − (βδ + αγ)xe−1.
Pantelimon Stănică
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A note on Fibonacci matrices of even degree
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 8, Page 457-469, 2001., 2001 This paper presents a construction of m‐by‐m irreducible Fibonacci matrices for any even m. The proposed technique relies on matrix representations of algebraic number fields which are an extension of the golden section field. The explicit construction of some 6‐by‐6 and 8‐by‐8 irreducible Fibonacci matrices is given.
Michele Elia
wiley +1 more source
On Fibonacci-type polynomial recurrences of order two and the accumulation points of their set of zeros [PDF]
, 2018 We identify the accumulation points of the zero set of the polynomial family Gn+1(z) := zGn(z) + Gn−1(z), n 2 N, generated from complex polynomial seeds G0,G1.
Batra, Prashant
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On the power sum problem of Lucas polynomials and its divisible property
Open Mathematics, 2018 The main purpose of this paper is to use the mathematical induction and the properties of Lucas polynomials to study the power sum problem of Lucas polynomials. In the end, we obtain an interesting divisible property.
Xiao Wang
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