Results 91 to 100 of about 1,240,504 (163)
Arctangent Identities Involving the Jacobsthal and Jacobsthal-Lucas Numbers
Electronic Journal of Mathematical Analysis and ApplicationsThis study presents novel arctangent identities that establish connections between the Jacobsthal and Jacobsthal-Lucas numbers. These findings contribute to the understanding of the interplay between trigonometric functions and number theory, particularly in relation to well-known mathematical sequences and constants.
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On characteristic polynomial of higher order generalized Jacobsthal numbers
Advances in Difference Equations, 2019 In this paper, we study a higher order generalization of the Jacobsthal sequence, namely, the (k,c) $(k,c)$-Jacobsthal sequence (Jn(k,c)) $(J^{(k,c)}_{n})$ for any integers n, k≥2 $k\geq 2$ and a real number c>0 $c>0$.
Diego Marques, Pavel Trojovský
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The Adjacency-Jacobsthal-Hurwitz type numbers
Filomat, 2018 In this paper, we define the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind. Then we give the exponential, combinatorial, permanental and determinantal representations and the Binet formulas of the adjacency-Jacobsthal-Hurwitz numbers of the first and second kind by the aid of the generating functions and the generating
Deveci, Ömür, Aküzüm, Yeşim
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Binomial sums with k-Jacobsthal and k-Jacobsthal–Lucas numbers
Notes on Number Theory and Discrete Mathematics, 2022 In this paper, we derive some important identities involving k-Jacobsthal and k-Jacobsthal–Lucas numbers. Moreover, we use multinomial theorem to obtain distinct binomial sums of k-Jacobsthal and k-Jacobsthal–Lucas numbers.
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Common Factors of Generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas numbers
International Journal of Applied Mathematical Research, 2012 In this paper, we present identities involving common factors of generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas numbers. Binet’s formula will employ to obtain the identities.
V. K. Gupta, Yashwant Kumar Panwar
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On Some Identities for k-Jacobsthal Numbers [PDF]
, 2013 The aim of this paper is to obtain Binet formula for k-Jacobsthal numbers. And also with the help of Binet formula we obtain some properties for the k-Jacobsthal numbers.
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Integral representations of the Jacobsthal and Jacobsthal-Lucas numbers
Our study aims to obtain integral representations of Jacobsthal J_kn and Jacobsthal-Lucas L_kn, and then to use these integral representations to derive integral representations of Jacobsthal J_kn+r and Jacobsthal-Lucas L_kn+r, where n\in Z_0={0,1,2,..} is a non-negative integer, k \in Z_>0=1,2,3,... is an arbitrary but fixed positive integer, while r
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On the Generalized Order-k Jacobsthal and Jacobtshal-Lucas Numbers
The classic Jacobsthal numbers were generalized to k sequences of the generalized order-k Jacobsthal numbers and then have been studied by several authors.
Ahmed, Hossen +2 more
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Some generalizations of the Jacobsthal numbers
, 2010 The main object of this paper is to introduce and investigate some proper- ties and relations involving sequences of numbers Fn,m(r), for m = 2, 3, 4, and r is some real number.
Gospava Djordjevic
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Triangle Geometry and Jacobsthal Numbers [PDF]
, 2003 The convergence properties of certain triangle centres on the Euler line of an arbitrary triangle are studied. Properties of the Jacobsthal numbers, which appear in this process, are examined, and a new formula is given.
Barry, Paul
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