Results 101 to 110 of about 973 (216)
Weighted sum of the sixth powers of Horadam numbers [PDF]
Notes on Number Theory and Discrete MathematicsOhtsuka and Nakamura found simple formulas for Σⁿⱼ₌₁Fⱼ⁶ and Σⁿⱼ₌₁Lⱼ⁶, where Fₖ and Lₖ are the k-th Fibonacci and Lucas numbers, respectively. In this note we extend their results to a general second order sequence by deriving a formula for Σⁿⱼ₌₁(-1/q³ ...
Kunle Adegoke +2 more
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International Journal of Analysis and Applications, 2013 In this paper, we present generalized identities involving common factors of generalized Fibonacci, Jacobsthal and jacobsthal-Lucas numbers. Binet’s formula will employ to obtain the identities.
Yashwant K. Panwar +2 more
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On the order-m generalized Fibonacci k-numbers
, 2009 In this paper, we defined order-m generalized Fibonacci k-numbers by matrix representation. Using this matrix representation we obtained sums, some identities and the generalized Binet formula of generalized order-m Fibonacci k-numbers. (C) 2009 Elsevier
Bozkurt, Durmus, Akbulak, Mehmet
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Restricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers
, 2005 In 1985 Simion and Schmidt showed that the number of permutations in Sn which avoid 132, 213, and 123 is equal to the Fibonacci number Fn+1. We use generating function and bijective techniques to give other sets of pattern-avoiding permutations which can be enumerated in terms of Fibonacci or k-generalized Fibonacci numbers.
Egge, Eric C., Mansour, Toufik
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9-Modularity and GCD Properties of Generalized Fibonacci Numbers
, 2014 : We study 9-modularity properties of generalized Fibonacci numbers that give rise to well-known quasigroups. In this paper we also study GCD and divisibility properties of generalized Fibonacci numbers.
Junes, Leandro +2 more
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SUM FORMULAE OF GENERALIZED FIBONACCI AND LUCAS NUMBERS
, 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.
Keskin, Refik +2 more
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Generalized Gaussian Fibonacci numbers and sums by matrix methods
, 2017 Many authors define certain generalizations of the usual Fibonacci, Pell and Lucas numbers by matrix methods and then obtain the Binet formulas and combinatorial representations of the generalizations of these number sequence.
Aşcı, Mustafa, Lee, G.Y.
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Some Finite Sums Involving Generalized Fibonacci and Lucas Numbers
Discrete Dynamics in Nature and Society, 2011 By considering Melham's sums (Melham, 2004), we compute various more general nonalternating sums, alternating sums, and sums that alternate according to (−1)2𝑛+1 involving the generalized Fibonacci and Lucas numbers.
E. Kılıç, N. Ömür, Y. T. Ulutaş
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Binomial transform of the generalized k-Fibonacci numbers
, 2019 We recall the concept and some properties of the generalized k-Fibonacci numbers and then apply the binomial transform to these sequences. As consequence, we obtain new integer sequences related to the generalized k -Fibonacci numbers.
Falcon, Sergio
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Generalized Fibonacci Dynamical Systems
, 2009 In this paper we consider generalizations of dynamical systems that are based on the Fibonacci sequence. We first study stability properties of such systems for both the continuous and discrete–time case.
Balestrino, A +2 more
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