Results 141 to 150 of about 1,180,296 (224)
Generalized Fibonacci numbers and automorphisms of K3 surfaces with Picard number 2 [PDF]
arXivUsing the properties of generalized Fibonacci numbers, we determine the automorphism groups of some K3 surfaces with Picard number 2. Conversely, using the automorphisms of K3 surfaces with Picard number 2, we prove the criterion for a given integer n is to be a generalized Fibonacci number.
arxiv
Remarks On General Fibonacci Numbers
, 2015 We dedicate this paper to investigate the most generalized form of Fibonacci Sequence, one of the most studied sections of the mathematical literature. One can notice that, we have discussed even a more general form of the conventional one. Although it seems the topic in the first section has already been covered before, but we present a different ...
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Sums of products of generalized Fibonacci and Lucas numbers
Acta Mathematica Hungarica, 2014 Sums of products of a fixed number of Fibonacci(-type) numbers can be computed automatically. This extends, at least in principle, various results about two factors that appeared in the literature. More general results (with an arbitrary number of factors) where then guessed and eventually proved by traditional ("human") methods.
Kılıç, Emrah, Prodinger, Helmut
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Some Theorems Involving Powers of Generalized Fibonacci Numbers at Non-Equidistant Points [PDF]
, 2007 Paul S. Bruckman, R. S. Melham
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The Matrix Sequence in terms of bi-periodic Fibonacci numbers [PDF]
arXiv, 2016 In this paper, we define the bi-periodic Fibonacci matrix sequence that represent bi-periodic Fibonacci numbers. Then, we investigate generating function, Binet formula and summations of bi-periodic Fibonacci matrix sequence. After that, we say that some behaviours of bi-periodic Fibonacci numbers also can be obtained by considering properties of this ...
arxiv
Generalized Fibonacci Sequences and Binet-Fibonacci Curves [PDF]
arXiv, 2017 We have studied several generalizations of Fibonacci sequences as the sequences with arbitrary initial values, the addition of two and more Fibonacci subsequences and Fibonacci polynomials with arbitrary bases. For Fibonacci numbers with congruent indices we derived general formula in terms of generalized Fibonacci polynomials and Lucas numbers.
arxiv
Generalized Natural Density $\DF(\mathfrak{F}_n)$ of Fibonacci Word [PDF]
arXivThis paper explores profound generalizations of the Fibonacci sequence, delving into random Fibonacci sequences, $k$-Fibonacci words, and their combinatorial properties. We established that the $n$-th root of the absolute value of terms in a random Fibonacci sequence converges to $1.13198824\ldots$, a symmetry identity for sums involving Fibonacci ...
arxiv
AxiomsIn this paper, by using q-integers and higher-order generalized Fibonacci numbers, we define the higher-order generalized Fibonacci quaternions with q-integer components. We give some special cases of these newly established quaternions.
Can Kızılateş +3 more
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The generalized bi-periodic Fibonacci quaternions and octonions [PDF]
arXiv, 2018 In this paper, we present a further generalization of the bi- periodic Fibonacci quaternions and octonions. We give the generating function, the Binet formula, and some basic properties of these quaternions and octonions. The results of this paper not only give a generalization of the bi-periodic Fibonacci quaternions and octonions, but also include ...
arxiv
On the distance between generalized Fibonacci numbers [PDF]
, 2015 Jhon J. Bravo +2 more
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