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1.
This paper presents two new identities involving generalized Fibonacci and generalized Lucas numbers. One of these identities generalize the two well-known identities of Sury and Marques which are recently developed. Some other interesting identities involving the famous numbers of Fibonacci, Lucas, Pell and Pell-Lucas numbers are also deduced as special cases of the two derived identities. Performing some mathematical operations on the introduced identities yield some other new identities involving generalized Fibonacci and generalized Lucas numbers. 相似文献
2.
利用组合数学的方法,得到了一些包含高阶Genocchi数和广义Lucas多项式的恒等式,并且由此建立了Fibonacci数与Riemann Zeta函数的关系式. 相似文献
3.
利用Pell方程的理论,讨论了与广义Lucas数有关的一些级数的取整值问题.在一定条件下,解决了一些级数的取整值问题. 相似文献
4.
Feng-Zhen Zhao Tianming Wang 《International Journal of Mathematical Education in Science & Technology》2013,44(6):913-919
In this note, using the theory of Pell equation, the authors discuss the integrity of certain series involving generalized Fibonacci and Lucas numbers. 相似文献
5.
In this paper, we obtain some new results on matrices related with Fibonacci numbers and Lucas numbers. Also, we derive the relation between Pell numbers and its companion sequence by using our representations. 相似文献
6.
The properties of continued fractions, generalized golden sections, and generalized Fibonacci and Lucas numbers are proved on the ground of the properties of subsemigroups of the group of invertible integer matrices. Some properties of special recurrent sequences are studied. A new proof of the Pisot-Vijayaraghavan theorem is given. Some connections between continued fractions and Pisot numbers are considered. Some unsolved problems are stated. 相似文献
7.
Mahmut Akyiğit Hidayet Hüda Kösal Murat Tosun 《Advances in Applied Clifford Algebras》2013,23(3):535-545
Starting from ideas given by Horadam in [5] , in this paper, we will define the split Fibonacci quaternion, the split Lucas quaternion and the split generalized Fibonacci quaternion. We used the well-known identities related to the Fibonacci and Lucas numbers to obtain the relations between the split Fibonacci, split Lucas and the split generalized Fibonacci quaternions. Moreover, we give Binet formulas and Cassini identities for these quaternions. 相似文献
8.
A. Plaza S. Falcón 《International Journal of Mathematical Education in Science & Technology》2013,44(4):563-566
This note shows a combinatorial approach to some identities for generalized Fibonacci numbers. While it is a straightforward task to prove these identities with induction, and also by arithmetical manipulations such as rearrangements, the approach used here is quite simple to follow and eventually reduces the proof to a counting problem. 相似文献
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10.
In this paper, we consider the usual and generalized order-k Fibonacci and Pell recurrences, then we define a new recurrence, which we call generalized order-k F–P sequence. Also we present a systematic investigation of the generalized order-k F–P sequence. We give the generalized Binet formula, some identities and an explicit formula for sums of the generalized order-k F–P sequence by matrix methods. Further, we give the generating function and combinatorial representations of these numbers. Also we present an algorithm for computing the sums of the generalized order-k Pell numbers, as well as the Pell numbers themselves. 相似文献
11.
将二项式系数的性质应用到Lucas数列的研究中,并结合Fibonacci数列与Lucas数列的恒等式得到几个有趣的Lucas数列的同余式. 相似文献
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13.
《Discrete Mathematics》2022,345(9):112891
We calculate moments of the so-called Kesten distribution by means of the expansion of the denominator of the density of this distribution and then integrate all summands with respect to the semicircle distribution. By comparing this expression with the formulae for the moments of Kesten's distribution obtained by other means, we find identities involving polynomials whose power coefficients are closely related to Catalan numbers, Catalan triangles, binomial coefficients. Finally, as applications of these identities we obtain various interesting relations between the aforementioned numbers, also concerning Lucas, Fibonacci and Fine numbers. 相似文献
14.
Iwona Włoch Urszula Bednarz Dorota Bród Andrzej Włoch Małgorzata Wołowiec-Musiał 《Discrete Applied Mathematics》2013,161(16-17):2695-2701
In this paper, we define a new kind of Fibonacci numbers generalized in the distance sense. This generalization is related to distance Fibonacci numbers and distance Lucas numbers, introduced quite recently. We also study distinct properties of these numbers for negative integers. Their representations and interpretations in graphs are also studied. 相似文献
15.
LIU Duan-sen LI Chao YANG Cun-dianInstitute of Mathematics Shangluo Teacher''''s College Shangluo China 《数学季刊》2004,19(1):67-68
By studying the properties of Chebyshev polynomials, some specific and meaningful identities for the calculation of square of Chebyshev polynomials, Fibonacci numbers and Lucas numbers are obtained. 相似文献
16.
《数学季刊》2020,(1)
The purpose of this paper is to give the extensions of some identities involving generalized Fibonacci and Lucas numbers with binomial coefficients.These results generalize the identities by Gulec,Taskara and Uslu in Appl.Math.Lett.23(2010) 68-72 and Appl.Math.Comput.220(2013) 482-486. 相似文献
17.
Mahmut Akyig̃it Hidayet Hüda Kösal Murat Tosun 《Advances in Applied Clifford Algebras》2014,24(3):631-641
In this paper, the Fibonacci generalized quaternions are introduced. We use the well-known identities related to the Fibonacci and Lucas numbers to obtain the relations regarding these quaternions. Furthermore, the Fibonacci generalized quaternions are classified by considering the special cases of quaternionic units. 相似文献
18.
Chuanan Wei 《Integral Transforms and Special Functions》2016,27(7):592-598
By applying the derivative operator to Minton and Karlsson's hypergeometric series identities, several interesting summation formulae involving generalized harmonic numbers are established. 相似文献
19.
A type of nonlinear expressions of Lucas sequences are established inspired by Hsu [A nonlinear expression for Fibonacci numbers and its consequences.J.Math.Res.Appl.,2012,32(6):654–658].Using the relationships between the Lucas sequence and other linear recurring sequences satisfying the same recurrence relation of order 2,i.e.,the Horadam sequences,we may transfer the identities of Lucas sequences to the latter. 相似文献
20.
Riordan矩阵的垂直一半和水平一半已经被许多学者分别研究过.本文给出了Riordan矩阵的$(m,r,s)$-halves的定义.利用此定义能够统一的讨论Riordan矩阵的垂直一半和水平一半.作为应用,通过对Pascal和Delannoy矩阵的$(m,r,s)$-halves的研究,可以得到了一些与Fibonacci, Pell和Jacobsthal序列相关的等式. 相似文献