Fibonacci numbers: A population dynamics perspective
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DOI: 10.1016/j.heliyon.2019.e01130
Abstract: Fibonacci numbers or Fibonacci sequence is among the most popular numbers or sequence in Mathematics. In this paper, we discuss the sequence in a population dynamics perspective. We discuss the early development of the sequence… read more here.
Keywords: fibonacci numbers; population dynamics; dynamics perspective; sequence ... See more keywords
Use of Fibonacci numbers in lipidomics – Enumerating various classes of fatty acids
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DOI: 10.1038/srep39821
Abstract: In lipid biochemistry, a fundamental question is how the potential number of fatty acids increases with their chain length. Here, we show that it grows according to the famous Fibonacci numbers when cis/trans isomerism is… read more here.
Keywords: fatty acids; use fibonacci; fibonacci numbers; numbers lipidomics ... See more keywords
The complex-type k-Fibonacci sequences and their applications
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DOI: 10.1080/00927872.2020.1834573
Abstract: Abstract In this article, we define the complex-type k-Fibonacci numbers and then give the relationships between the k-step Fibonacci numbers and the complex-type k-Fibonacci numbers. Also, we obtain miscellaneous properties of the complex-type k-Fibonacci numbers… read more here.
Keywords: fibonacci sequences; fibonacci numbers; complex type; type fibonacci ... See more keywords
On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3
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DOI: 10.1142/s1793042120500876
Abstract: For an integer [Formula: see text], let [Formula: see text] be the [Formula: see text]-generalized Fibonacci sequence which starts with [Formula: see text] (a total of [Formula: see text] terms) and for which each term… read more here.
Keywords: fibonacci numbers; generalized fibonacci; problem pillai; formula see ... See more keywords
Diophantine quadruples with values in k-generalized Fibonacci numbers
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DOI: 10.1515/ms-2017-0156
Abstract: Abstract We consider for integers k ≥ 2 the k–generalized Fibonacci sequences F(k) := (Fn(k))n≥2−k, $\begin{array}{} (F_n^{(k)})_{n\geq 2-k}, \end{array} $ whose first k terms are 0, …, 0, 1 and each term afterwards is the… read more here.
Keywords: quadruples values; fibonacci numbers; generalized fibonacci; diophantine quadruples ... See more keywords
Fibonacci numbers in generalized Pell sequences
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DOI: 10.1515/ms-2017-0413
Abstract: Abstract In this paper, by using lower bounds for linear forms in logarithms of algebraic numbers and the theory of continued fractions, we find all Fibonacci numbers that appear in generalized Pell sequences. Some interesting… read more here.
Keywords: numbers generalized; pell sequences; fibonacci numbers; generalized pell ... See more keywords
Solutions of a generalized markoff equation in Fibonacci numbers
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DOI: 10.1515/ms-2017-0414
Abstract: Abstract In this paper, we find all the solutions (X, Y, Z) = (FI, FJ, FK), where FI, FJ, and FK represent nonzero Fibonacci numbers, satisfying a generalization of Markoff equation called the Jin-Schmidt equation:… read more here.
Keywords: generalized markoff; markoff equation; fibonacci numbers; solutions generalized ... See more keywords
k−Fibonacci numbers close to a power of 2
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DOI: 10.2989/16073606.2020.1818645
Abstract: A generalization of the well-known Fibonacci sequence is the k-generalized Fibonacci sequence whose first k terms are 0, . . . , 0, 1 and each term afterwards is the sum of the preceding k… read more here.
Keywords: numbers close; fibonacci numbers; close power;
On the Generalized Gaussian Fibonacci Numbers and Horadam Hybrid Numbers: A Unified Approach
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DOI: 10.3390/axioms11060255
Abstract: In this paper, we consider an approach based on the elementary matrix theory. In other words, we take into account the generalized Gaussian Fibonacci numbers. In this context, we consider a general tridiagonal matrix family.… read more here.
Keywords: fibonacci numbers; gaussian fibonacci; horadam hybrid; hybrid numbers ... See more keywords
Iterated Partial Sums of the k-Fibonacci Sequences
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DOI: 10.3390/axioms11100542
Abstract: In this paper, we find the sequence of partial sums of the k-Fibonacci sequence, say, Sk,n=∑j=1nFk,j, and then we find the sequence of partial sums of this new sequence, Sk,n2)=∑j=1nSk,j, and so on. The iterated… read more here.
Keywords: fibonacci numbers; sequence; sums fibonacci; iterated partial ... See more keywords
A new formula for hyper-Fibonacci numbers, and the number of occurrences
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DOI: 10.3906/mat-1607-13
Abstract: In this paper, we develop a new formula for hyper-Fibonacci numbers F [k] n , wherein the coefficients (related to Stirling numbers of the first kind) of the polynomial ingredient pk(n) are determined. As an… read more here.
Keywords: hyper fibonacci; formula hyper; fibonacci numbers; number occurrences ... See more keywords