Results 21 to 30 of about 189 (146)
On the higher power sums of reciprocal higher-order sequences. [PDF]
ScientificWorldJournal, 2014 Let {un} be a higher‐order linear recursive sequence. In this paper, we use the properties of error estimation and the analytic method to study the reciprocal sums of higher power of higher‐order sequences. Then we establish several new and interesting identities relating to the infinite and finite sums.
Wu Z, Zhang J.
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Unrestricted Tribonacci and Tribonacci–Lucas quaternions [PDF]
, 2023 We define a generalization of Tribonacci and Tribonacci-Lucas quaternions with arbitrary Tribonacci numbers and Tribonacci-Lucas numbers coefficients, respectively. We get generating functions and Binet's formulas for these quaternions.
Gonca Kızılaslan +3 more
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Some geometric properties of the Padovan vectors in Euclidean 3-space [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Padovan numbers were defined by Stewart (1996) in honor of the modern architect Richard Padovan (1935) and were first discovered in 1924 by Gerard Cordonnier.
Serdar Korkmaz, Hatice Kuşak Samancı
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On New Banach Sequence Spaces Involving Leonardo Numbers and the Associated Mapping Ideal
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 In the present study, we have constructed new Banach sequence spaces ℓpL,c0L,cL, and ℓ∞L, where L=lv,k is a regular matrix defined by lv,k=lk/lv+2−v+2, 0≤k≤v,0, k>v, for all v, k = 0, 1, 2, ⋯, where l=lk is a sequence of Leonardo numbers. We study their topological and inclusion relations and construct Schauder bases of the sequence spaces ℓpL,c0L, and
Taja Yaying +4 more
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Dold sequences, periodic points, and dynamics
Bulletin of the London Mathematical Society, Volume 53, Issue 5, Page 1263-1298, October 2021., 2021 Abstract In this survey we describe how the so‐called Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.
Jakub Byszewski +2 more
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Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 We use a new method of matrix decomposition for r‐circulant matrix to get the determinants of An = Circr(F1, F2, …, Fn) and Bn = Circr(L1, L2, …, Ln), where Fn is the Fibonacci numbers and Ln is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived.
Jiangming Ma +3 more
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On square Tribonacci Lucas numbers
Hacettepe Journal of Mathematics and Statistics, 2021 The Tribonacci-Lucas sequence {Sn}{Sn} is defined by the recurrence relation Sn+3=Sn+2+Sn+1+SnSn+3=Sn+2+Sn+1+Sn with S0=3, S1=1, S2=3.S0=3, S1=1, S2=3. In this note, we show that 11 is the only perfect square in Tribonacci-Lucas sequence for n≢1(mod32)n≢1(mod32) and n≢17(mod96).n≢17(mod96).
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Research on splitting quaternions with generalized Tribonacci hybrid number components [PDF]
Notes on Number Theory and Discrete MathematicsThis paper introduces the Generalized Tribonacci Hybrid Split Quaternion (GTHSQ), a novel split quaternion with coefficients derived from generalized Tribonacci hybrid numbers.
Yanni Yang, Yong Deng
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On Repdigits as Sums of Fibonacci and Tribonacci Numbers [PDF]
Symmetry, 2020 In this paper, we use Baker’s theory for nonzero linear forms in logarithms of algebraic numbers and a Baker-Davenport reduction procedure to find all repdigits (i.e., numbers with only one distinct digit in its decimal expansion, thus they can be seen as the easiest case of palindromic numbers, which are a ”symmetrical” type of numbers) that can be ...
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Tribonacci and Tribonacci-Lucas numbers via the determinants of special matrices
Applied Mathematical Sciences, 2014 In this paper, by using determinants of special matrices, it has been mainly obtained Tribonacci and Tribonacci-Lucas numbers. © 2014 Nazmiye Yilmaz and Necati Taskara.
Yilmaz N., Taskara N.
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