Results 31 to 40 of about 48,003 (223)
A Quadratic Diophantine Equation Involving Generalized Fibonacci Numbers
Mathematics, 2020 The sequence of the k-generalized Fibonacci numbers ( F n ( k ) ) n is defined by the recurrence F n ( k ) = ∑ j = 1 k F n − j ( k ) beginning with the k terms 0 , … , 0 , 1 .
Ana Paula Chaves, Pavel Trojovský
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Some identities for generalized Fibonacci and Lucas numbers [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 In this paper we study one parameter generalization of the Fibonacci numbers, Lucas numbers which generalizes the Jacobsthal numbers, Jacobsthal–Lucas numbers simultaneously. We present some their properties and interpretations also in graphs.
Anetta Szynal-Liana +2 more
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On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of Σn k=0 kW3 k and Σn k=1 kW3− k
Asian Research Journal of Mathematics, 2020 In this paper, closed forms of the sum formulas Σn k=0 kW3 k and Σn k=1 kW3-k for the cubes of generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.
Y. Soykan
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Determinants Containing Powers of Generalized Fibonacci Numbers [PDF]
, 2015 We study determinants of matrices whose entries are powers of Fibonacci numbers. We then extend the results to include entries that are powers of generalized Fibonacci numbers defined as a second-order linear recurrence relation. These studies have led us to discover a fundamental identity of determinant involving powers of linear polynomials. Finally,
Aram Tangboonduangjit +1 more
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Advances in Research, 2020 In this paper, closed forms of the summation formulas for generalized Fibonacci and Gaussian generalized Fibonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results.
Y. Soykan
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International Journal of Analysis and Applications, 2013 In this paper, we present generalized identities involving common factors of generalized Fibonacci, Jacobsthal and jacobsthal-Lucas numbers. Binet’s formula will employ to obtain the identities.
Yashwant K. Panwar +2 more
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On the growth rate of generalized Fibonacci numbers
Advances in Difference Equations, 2004 Let α(t) be the limiting ratio of the generalized Fibonacci numbers produced by summing along lines of slope t through the natural arrayal of Pascal's triangle. We prove that is an even function.
Fishkind Donniell E
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Dynamic Organization of Cells in Colonic Epithelium is Encoded by Five Biological Rules. [PDF]
Biol CellThis study reports that a set of five biological rules encodes how colonic epithelium dynamically maintains its precise organization of cells despite continuous tissue renewal. These rules might even provide a means to understand the mechanisms that underlie organization of other tissue types, and how tissue disorganization leads to birth defects and ...
Boman BM +8 more
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Mathematics, 2021 In this paper, we introduce and study a new two-parameters generalization of the Fibonacci numbers, which generalizes Fibonacci numbers, Pell numbers, and Narayana numbers, simultaneously.
Natalia Bednarz
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On generalized Fibonacci numbers [PDF]
Applied Mathematical Sciences, 2015 We provide a formula for the $n^{th}$ term of the $k$-generalized Fibonacci-like number sequence using the $k$-generalized Fibonacci number or $k$-nacci number, and by utilizing the newly derived formula, we show that the limit of the ratio of successive terms of the sequence tends to a root of the equation $x + x^{-k} = 2$.
Bacani, Jerico B. +1 more
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