Results 31 to 40 of about 3,822 (183)
Melham's sums for some Lucas polynomial sequences [PDF]
Notes on Number Theory and Discrete MathematicsA Lucas polynomial sequence is a pair of generalized polynomial sequences that satisfy the Lucas recurrence relation. Special cases include Fibonacci polynomials, Lucas polynomials, and Balancing polynomials.
Chan-Liang Chung, Chunmei Zhong
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On Generalized Jacobsthal and Jacobsthal–Lucas Numbers
Annales Mathematicae Silesianae, 2022 Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers.
Bród Dorota, Michalski Adrian
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A Family of the Zeckendorf Theorem Related Identities [PDF]
, 2015 In this paper we present a family of identities for recursive sequences arising from a second order recurrence relation, that gives instances of Zeckendorf representation.
Martinjak, Ivica
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Derivative Sequences of Fibonacci and Lucas Polynomials [PDF]
, 1991 Let us consider the Fibonacci polynomials U n(x) and the Lucas polynomials V n (x) (or simply U n and Vn, if there is no danger of confusion) defined as $$ {U_n} = x{U_{n - 1}} + {U_{n - 2}}({U_0} = 0,{U_1} = 1) $$ (1.1) and $$ {V_n} = x{V_{n - 2}}({V_0} = 2,V = x) $$ (1.2) where x is an indeterminate.
Piero Filipponi, Alwyn F. Horadam
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Divisibility Properties of the Fibonacci, Lucas, and Related Sequences [PDF]
ISRN Algebra, 2014 We use matrix techniques to give simple proofs of known divisibility properties of the Fibonacci, Lucas, generalized Lucas, and Gaussian Fibonacci numbers. Our derivations use the fact that products of diagonal matrices are diagonal together with Bezout’s identity.
Thomas Jeffery, Rajesh Pereira
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On Generalized Lucas Pseudoprimality of Level k
Mathematics, 2021 We investigate the Fibonacci pseudoprimes of level k, and we disprove a statement concerning the relationship between the sets of different levels, and also discuss a counterpart of this result for the Lucas pseudoprimes of level k.
Dorin Andrica, Ovidiu Bagdasar
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Diophantine equations involving the bi-periodic Fibonacci and Lucas sequences
Acta et Commentationes Universitatis Tartuensis de Mathematica, 2022 In this paper, we present new identities involving the biperiodic Fibonacci and Lucas sequences. Then we solve completely some quadratic Diophantine equations involving the bi-periodic Fibonacci and Lucas sequences.
Ait-Amrane, Lyes +2 more
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A Matrix Approach for Divisibility Properties of the Generalized Fibonacci Sequence
Discrete Dynamics in Nature and Society, 2013 We give divisibility properties of the generalized Fibonacci sequence by matrix methods. We also present new recursive identities for the generalized Fibonacci and Lucas sequences.
Aynur Yalçiner
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Exploring Generalized $2^k$-Fibonacci Sequence: A New Family of the Fibonacci Sequence
Communications in Advanced Mathematical SciencesThe focus of this paper is to study the $2^k$–Fibonacci sequence, which is defined for all integers $2^k$, and its connections with both the Fibonacci and the Fibonacci-Lucas sequences.
Elis Gardel Costa Mesquista +2 more
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On sums of k-generalized Fibonacci and k-generalized Lucas numbers as first and second kinds of Thabit numbers [PDF]
Notes on Number Theory and Discrete MathematicsLet (Fᵣ⁽ᵏ⁾)ᵣ≥2-k and (Lᵣ⁽ᵏ⁾)ᵣ≥2-k be generalizations of the Fibonacci and Lucas sequences, where k≥2. For these sequences the initial k terms are 0,0,...,0, 1 and 0,0,...,2,1, and each subsequent term is the sum of the preceding k terms.
Hunar Sherzad Taher, Saroj Kumar Dash
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