scholarly journals Some Identities Involving the Generalized Lucas Numbers

2020 ◽  
Vol 9 (1) ◽  
pp. 11-15
Author(s):  
Mansi S. Shah Mansi S. Shah ◽  
Devbhadra V. Shah Devbhadra V. Shah
Keyword(s):  
Lucas Numbers ◽  
Generalized Lucas Numbers

scholarly journals A curious property of series involving terms of generalized sequences

2000 ◽  
Vol 23 (1) ◽  
pp. 55-63
Author(s):  
Odoardo Brugia ◽  
Piero Filipponi
Keyword(s):  
Fibonacci Numbers ◽  
Fibonacci Number ◽  
Lucas Numbers ◽  
Generalized Fibonacci Numbers ◽  
Generalized Lucas Numbers ◽  
Curious Property

Here we are concerned with series involving generalized Fibonacci numbersUn  (p,q)and generalized Lucas numbersVn  (p,q). The aim of this paper is to find triples(p,q,r)for which the seriesUn  (p,q)/rnandVn  (p,q)/rn(forrrunning from 0 to infinity) are unconcerned at the introduction of the factorn. The results established in this paper generalize the known fact that the seriesFn/2n(Fnthenth Fibonacci number) and the seriesnFn/2ngive the same result, namely−2/5.

scholarly journals Pythagorean triples containing generalized Lucas numbers

2018 ◽  
Vol 42 (4) ◽  
pp. 1904-1912
Author(s):  
Zafer ŞİAR ◽  
Refik KESKİN
Keyword(s):  
Lucas Numbers ◽  
Pythagorean Triples ◽  
Generalized Lucas Numbers

On the order-k generalized Lucas numbers

2004 ◽  
Vol 155 (3) ◽  
pp. 637-641 ◽  
Author(s):  
Dursun Tasci ◽  
Emrah Kilic
Keyword(s):  
Lucas Numbers ◽  
Generalized Lucas Numbers

scholarly journals Generalized Lucas numbers of the form 3 × 2^m

2021 ◽  
Vol 27 (2) ◽  
pp. 129-136
Author(s):  
Salah Eddine Rihane ◽  
◽  
Chefiath Awero Adegbindin ◽  
Alain Togbé ◽  
◽  
...  
Keyword(s):  
Diophantine Equation ◽  
Lucas Numbers ◽  
Lucas Sequence ◽  
Generalized Lucas Numbers ◽  
Positive Integers

For an integer $k\geq 2$, let $(L_n^{(k)})_n$ be the k-generalized Lucas sequence which starts with $0,\ldots,0,2,1$ (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we look the k-generalized Lucas numbers of the form $3\times 2^m$ i.e. we study the Diophantine equation $L^{(k)}_n = 3\times 2^m$ in positive integers n, k, m with $k \geq 2$.

scholarly journals Some properties of the generalized Fibonacci and Lucas numbers

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2655-2665
Author(s):  
Gospava Djordjevic ◽  
Snezana Djordjevic
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Fibonacci Numbers ◽  
Lucas Numbers ◽  
Generalized Fibonacci Numbers ◽  
Generalized Lucas Numbers ◽  
Fibonacci And Lucas Numbers

In this paper we consider the generalized Fibonacci numbers Fn,m and the generalized Lucas numbers Ln,m. Also, we introduce new sequences of numbers An,m, Bn,m, Cn,m and Dn,m. Further, we find the generating functions and some recurrence relations for these sequences of numbers.

Generalized Lucas Numbers of the form $wx^{2}$ and $wV_{m}x^{2}$

2018 ◽  
Vol 47 (3) ◽  
pp. 465-480
Author(s):  
Merve GÜNEY DUMAN ◽  
Ümmügülsüm ÖĞÜT ◽  
Refik KESKİN
Keyword(s):  
Lucas Numbers ◽  
Generalized Lucas Numbers

scholarly journals Determinants, Norms, and the Spread of Circulant Matrices with Tribonacci and Generalized Lucas Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Juan Li ◽  
Zhaolin Jiang ◽  
Fuliang Lu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Circulant Matrix ◽  
Circulant Matrices ◽  
Lucas Numbers ◽  
Partial Differential ◽  
Tribonacci Numbers ◽  
Generalized Lucas Numbers

Circulant matrices play an important role in solving ordinary and partial differential equations. In this paper, by using the inverse factorization of polynomial of degreen, the explicit determinants of circulant and left circulant matrix involving Tribonacci numbers or generalized Lucas numbers are expressed in terms of Tribonacci numbers and generalized Lucas numbers only. Furthermore, four kinds of norms and bounds for the spread of these matrices are given, respectively.

Generalized Lucas Numbers Which are Concatenations of Two Repdigits

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Eric F. Bravo ◽  
Jhon J. Bravo ◽  
Carlos A. Gómez
Keyword(s):  
Lucas Numbers ◽  
Generalized Lucas Numbers
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