Results 11 to 20 of about 757 (89)
On the sum of reciprocal generalized Fibonacci numbers [PDF]
, 2014 In this paper, we consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers.
He, Zilong, Yuan, Pingzhi, Zhuo, Junyi
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On the Partial Finite Alternating Sums of Reciprocals of Balancing and Lucas-Balancing Numbers
Discussiones Mathematicae - General Algebra and Applications, 2020 In this note, the finite alternating sums of reciprocals of balancing and Lucas-balancing numbers are considered and several identities involving these sums are deduced.
Dutta Utkal Keshari, Ray Prasanta Kumar
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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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Special Matrices, 2023 Denote by σn{\sigma }_{n} the n-th Stirling polynomial in the sense of the well-known book Concrete Mathematics by Graham, Knuth and Patashnik. We show that there exist developments xσn(x)=∑j=0n(2jj!)−1qn−j(j)xjx{\sigma }_{n}\left(x)={\sum }_{j=0}^{n ...
Kovačec Alexander +1 more
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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 rationality condition for the existence of odd perfect numbers
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 20, Page 1261-1293, 2003., 2003 A rationality condition for the existence of odd perfect numbers is used to derive an upper bound for the density of odd integers such that σ(N) could be equal to 2N, where N belongs to a fixed interval with a lower limit greater than 10300. The rationality of the square root expression consisting of a product of repunits multiplied by twice the base ...
Simon Davis
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Discussiones Mathematicae - General Algebra and Applications, 2018 In this paper we introduce the Horadam hybrid numbers and give some their properties: Binet formula, character and generating function.
Szynal-Liana Anetta
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Fascinating Number Sequences from Fourth Order Difference Equation Via Quaternion Algebras
Discussiones Mathematicae - General Algebra and Applications, 2021 The balancing and Lucas-balancing numbers are solutions of second order recurrence relations. A linear combination of these numbers can also be obtained as solutions of a fourth order recurrence relation.
Patra Asim
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Dynamics of a certain sequence of powers
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 4, Page 283-288, 2000., 2000 For any nonzero complex number z we define a sequence a1(z) = z, a2(z)=za1(z),…,an+1(z)=zan(z), n ∈ ℕ. We attempt to describe the set of these z for which the sequence {an(z)} is convergent. While it is almost impossible to characterize this convergence set in the complex plane 𝒞, we achieved it for positive reals.
Roman Sznajder, Kanchan Basnyat
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On a conjecture about generalized Q-recurrence
Open Mathematics, 2018 Chaotic meta-Fibonacci sequences which are generated by intriguing examples of nonlinear recurrences still keep their mystery although substantial progress has been made in terms of well-behaved solutions of nested recurrences.
Alkan Altug
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