Results 101 to 110 of about 1,912,276 (202)
Restricted Binary Strings and Generalized Fibonacci Numbers [PDF]
, 2017 We provide some interesting relations involving k-generalized Fibonacci numbers between the set \(F_n^{(k)}\) of length n binary strings avoiding k of consecutive 0’s and the set of length n strings avoiding \(k+1\) consecutive 0’s and 1’s with some more restriction on the first and last letter, via a simple bijection.
openaire +3 more sources
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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Closed forms for 10 families of finite sums of fractional generalized Fibonacci products [PDF]
, 2018 © 2018 The Fibonacci Association. All rights reserved. In this paper, we present closed forms for 10 families of finite sums where the denominator of the summand is a product of generalized Fibonacci numbers.
Melham, RS
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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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Some conjectures concerning sums of odd powers of Fibonacci and Lucas numbers
, 2009 This paper contains observations, conjectures and open questions concerning two finite sums that involve Fibonacci and Lucas numbers. Certain authors have become aware of the contents of this 9hitherto unpublished) manuscript and have made inroads into ...
Melham, R
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On the Sequences of $(q,k)$-Generalized Fibonacci Numbers
, 2022 In this paper, we consider the new family of recurrence sequences of $(q,k)$-generalized Fibonacci numbers. These sequences naturally extend the well-known sequences of $k$-generalized Fibonacci numbers and generalized $k$-order Pell numbers.
Kreutz, Alessandra +3 more
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Alternating sums of reciprocal generalized Fibonacci numbers. [PDF]
Springerplus, 2014 Kuhapatanakul K.
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Simplicial $d$-Polytopic Numbers Defined on Generalized Fibonacci Polynomials [PDF]
In this article, we introduce the simplicial $d$-polytopic numbers defined on generalized Fibonacci polynomials. We establish basic identities and find $q$-identities known.
López, Ronald Orozco
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AxiomsIn this paper, by using q-integers and higher-order generalized Fibonacci numbers, we define the higher-order generalized Fibonacci quaternions with q-integer components. We give some special cases of these newly established quaternions.
Can Kızılateş +3 more
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On Generalized Metallic Leonardo Numbers: Silver, Bronze, and Copper Cases
Universal Journal of Mathematics and ApplicationsIn this article, we discuss three new extensions of the Leonardo numbers in a generalized way, which we call the generalized Silver, Bronze, and Copper Leonardo numbers that converge to the Silver, Bronze, and Copper ratios, unifying existing metallic ...
Munesh Kumari +2 more
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