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Search Results: 1 - 10 of 3370 matches for " generalized Fibonacci numbers "
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The Finite Sum Formula for Generalized Fibonacci Numbers
ZHANG Fu-ling
Journal of Chongqing Normal University , 2011,
Abstract: In the paper, defining the Generalized Fibonacci Sequences * The general formula of Generalized Fibonacci Sequences * is given by using characteristic equation. Using the recurrence property of generalized Fibonacci Sequences, this article provides the some finite sum formulas which are * for generalized Fibonacci Sequences, promoting the conclusion of Generalized Fibonacci Seqquences.(* Indicates a formula, please see the full text)
On the k-Generalized Fibonacci Numbers
Nazmiye Y?lmaz,Yasin Yazl?k,Necati Ta?kara
Sel?uk Journal of Applied Mathematics , 2012,
Abstract: In this paper, we define a new family of k-generalized Fibonacci numbers. Furthermore, we give sums and recurrence relations of this numbers and obtain generating functions of this numbers for k=2.
On the properties of generalized fibonacci numbers with binomial coefficients

张彩环,刘 栋
ZHANG Caihuan
,LIU Dong

- , 2017,
Abstract: 该文通过研究广义的Fibonacci数,得到了许多重要的性质,并且,用二项式系数对广义Fibonacci数的一些性质进行了概括.
Roman Witula,Damian Slota
Applicable Analysis and Discrete Mathematics , 2009, DOI: 10.2298/aadm0902310w
Abstract: The scope of the paper is the definition and discussion of the polynomial generalizations of the {sc Fibonacci} numbers called here $delta$-{sc Fibonacci} numbers. Many special identities and interesting relations for these new numbers are presented. Also, different connections between $delta$-{sc Fibonacci} numbers and {sc Fibonacci} and {sc Lucas} numbersare proven in this paper.
On the k–Lucas Numbers of Arithmetic Indexes  [PDF]
Sergio Falcon
Applied Mathematics (AM) , 2012, DOI: 10.4236/am.2012.310175
Abstract: In this paper, we study the k–Lucas numbers of arithmetic indexes of the form an+r , where n is a natural number and r is less than r. We prove a formula for the sum of these numbers and particularly the sums of the first k-Lucas numbers, and then for the even and the odd k-Lucas numbers. Later, we find the generating function of these numbers. Below we prove these same formulas for the alternated k-Lucas numbers. Then, we prove a relation between the k–Fibonacci numbers of indexes of the form 2rn and the k–Lucas numbers of indexes multiple of 4. Finally, we find a formula for the sum of the square of the k-Fibonacci even numbers by mean of the k–Lucas numbers.
Sums of Squares of Fibonacci Numbers with Prime Indices  [PDF]
A. Gnanam, B. Anitha
Journal of Applied Mathematics and Physics (JAMP) , 2015, DOI: 10.4236/jamp.2015.312186
Abstract: In this paper we present some identities for the sums of squares of Fibonacci and Lucas numbers with consecutive primes, using maximal prime gap G(x)~log2x, as indices.
Fibonacci Congruences and Applications  [PDF]
René Blacher
Open Journal of Statistics (OJS) , 2011, DOI: 10.4236/ojs.2011.12015
Abstract: When we study a congruence T(x) ≡ ax modulo m as pseudo random number generator, there are several means of ensuring the independence of two successive numbers. In this report, we show that the dependence depends on the continued fraction expansion of m/a. We deduce that the congruences such that m and a are two successive elements of Fibonacci sequences are those having the weakest dependence. We will use this result to obtain truly random number sequences xn. For that purpose, we will use non-deterministic sequences yn. They are transformed using Fibonacci congruences and we will get by this way sequences xn. These sequences xn admit the IID model for correct model.
Relationships between Some k -Fibonacci Sequences  [PDF]
Sergio Falcon
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.515216
Abstract: In this paper, we will see that some -Fibonacci sequences are related to the classical Fibonacci sequence of such way that we can express the terms of a k -Fibonacci sequence in function of some terms of the classical Fibonacci sequence. And the formulas will apply to any sequence of a certain set of k' -Fibonacci sequences. Thus we find k -Fibonacci sequences relating to other k -Fibonacci sequences when σ'k is linearly dependent of \"\".
Squares from D(–4) and D(20) Triples  [PDF]
Zvonko ?erin
Advances in Pure Mathematics (APM) , 2011, DOI: 10.4236/apm.2011.15052
Abstract: We study the eight infinite sequences of triples of natural numbers A=(F2n+1,4F2n+3,F2n+7), B=(F2n+1,4F2n+5,F2n+7), C=(F2n+1,5F2n+1,F2n+3), D=(F2n+3,4F2n+1,F2n+3) and A=(L2n+1,4L2n+3,L2n+7), B=(L2n+1,4L2n+5,L2n+7), C=(L2n+1,5L2n+1,L2n+3), D=(L2n+3,4L2n+1,L2n+3. The sequences A,B,C and D are built from the Fibonacci numbers Fn while the sequences A, B, C and D from the Lucas numbers Ln. Each triple in the sequences A,B,C and D has the property D(-4) (i. e., adding -4 to the product of any two different components of them is a square). Similarly, each triple in the sequences A, B, C and D has the property D(20). We show some interesting properties of these sequences that give various methods how to get squares from them.
On the Norms of r-Hankel Matrices Involving Fibonacci and Lucas Numbers  [PDF]
Hasan G?kba?, Hasan K?se
Journal of Applied Mathematics and Physics (JAMP) , 2018, DOI: 10.4236/jamp.2018.67117
Abstract: Let us define A=Hr=(aij)to be n×nr-Hankel matrix. The entries of matrix A are Fn=Fi+j-2?or Ln=Fi+j-2?where Fn?and Ln?denote the usual Fibonacci and Lucas numbers, respectively. Then, we obtained upper and lower bounds for the spectral norm of matrix A. We compared our bounds with exact value of matrix A’s spectral norm. These kinds of matrices have
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