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1.
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
2.
Kantaphon Kuhapatanakul 《International Journal of Mathematical Education in Science & Technology》2013,44(8):1228-1234
In this note, we study the Fibonacci and Lucas p-numbers. We introduce the Lucas p-matrix and companion matrices for the sums of the Fibonacci and Lucas p-numbers to derive some interesting identities of the Fibonacci and Lucas p-numbers. 相似文献
3.
W.M. Abd-Elhameed N.A. Zeyada 《International Journal of Mathematical Education in Science & Technology》2017,48(1):102-107
This paper is concerned with developing a new class of generalized numbers. The main advantage of this class is that it generalizes the two classes of generalized Fibonacci numbers and generalized Pell numbers. Some new identities involving these generalized numbers are obtained. In addition, the two well-known identities of Sury and Marques which are recently developed are deduced as special cases. Moreover, some other interesting identities involving the celebrated Fibonacci, Lucas, Pell and Pell–Lucas numbers are also deduced. 相似文献
4.
For the incomplete Fibonacci and incomplete Lucas numbers, which were introduced and studied recently by P. Filliponi [Rend. Circ. Math. Palermo (2)45 (1996), 37–56], the authors derive two classes of generating functions in terms of the familiar Fibonacci and Lucas numbers,
respectively. 相似文献
5.
Refik Keskin 《International Journal of Mathematical Education in Science & Technology》2013,44(3):379-387
The aim of this article is to characterize the 2 × 2 matrices X satisfying X 2 = X + I and obtain some new identities concerning with Fibonacci and Lucas numbers. 相似文献
6.
The aim of this paper is to give new results about factorizations of the Fibonacci numbers F
n
and the Lucas numbers L
n
. These numbers are defined by the second order recurrence relation a
n+2 = a
n+1+a
n
with the initial terms F
0 = 0, F
1 = 1 and L
0 = 2, L
1 = 1, respectively. Proofs of theorems are done with the help of connections between determinants of tridiagonal matrices
and the Fibonacci and the Lucas numbers using the Chebyshev polynomials. This method extends the approach used in [CAHILL,
N. D.—D’ERRICO, J. R.—SPENCE, J. P.: Complex factorizations of the Fibonacci and Lucas numbers, Fibonacci Quart. 41 (2003), 13–19], and CAHILL, N. D.—NARAYAN, D. A.: Fibonacci and Lucas numbers as tridiagonal matrix determinants, Fibonacci Quart. 42 (2004), 216–221]. 相似文献
7.
In this article, we find elements of the Lucas polynomials by using two matrices. We extend the study to the n-step Lucas polynomials. Then the Lucas polynomials and their relationship are generalized in the paper. Furthermore, we give relationships between the Fibonacci polynomials and the Lucas polynomials. 相似文献
8.
9.
Modern natural science requires the development of new mathematical apparatus. The generalized Fibonacci numbers or Fibonacci p-numbers (p = 0, 1, 2, 3, …), which appear in the “diagonal sums” of Pascal’s triangle and are assigned in the recurrent form, are a new mathematical discovery. The purpose of the present article is to derive analytical formulas for the Fibonacci p-numbers. We show that these formulas are similar to the Binet formulas for the classical Fibonacci numbers. Moreover, in this article, there is derived one more class of the recurrent sequences, which is defined to be a generalization of the Lucas numbers (Lucas p-numbers). 相似文献
10.
11.
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
12.
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
13.
I. J. Good 《The Journal of the Operational Research Society》1992,43(8):837-842
The connections between the Golden Ratio namely (1 + √5)/2, a simple continued fraction, and Fibonacci and Lucas numbers, are familiar. The Fibonacci and Lucas numbers have many fascinating properties. We now point out that the square root of the Golden Ratio is the real part of a simple periodic continued fraction but using (complex) Gaussian integers a + ib instead of the natural integers. This fact provokes a definition and a study of complex Fibonacci and Lucas numbers, and the study again turns out to have a rich theoretic structure. A fuller account will appear in The Fibonacci Quarterly. 相似文献
14.
Ludwig Baringhaus 《Proceedings of the American Mathematical Society》1996,124(12):3875-3884
We study the distributions of integrals of Gaussian processes arising as limiting distributions of test statistics proposed for treating a goodness of fit or symmetry problem. We show that the cumulants of the distributions can be expressed in terms of Fibonacci numbers and Lucas numbers.
15.
16.
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
17.
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
18.
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
19.
《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
20.
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