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5 articles for “Fibonacci Sequences”
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New Number Sequences Obtained with Grouping of Fibonacci Numbers
Abstract: AbstractThe relations of the sum and difference of two Fibonacci numbers, in which the difference of subscripts is even, was given by Koshy. In this study, the relations of the sum and difference of two Fibonacci numbers, in which is the difference of subscripts is odd, is introduced by using the generating functions. Similar results are given for Lucas numbers. Also, two new family of Fibonacci numbers are obtained. Keywords: …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 7, Issue 3, 2020 · pp. 27–35 Read article
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New Recurrence Relations for Tribonacci Sequence and Generalized Tribonacci Sequence
Abstract: AbstractTribonacci numbers are placed on the corners of polygons clockwise with each corner receiving a term. Then, it is argued whether there is a relationship among the numbers in the same corners. It is shown to be able to find mth term corresponding to the corner Ak in an n-gon by a relation:where, is a Tribonaccisequence and is a Tribonacci- Lucas sequence. The relation is proved by using a binet …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 7, Issue 3, 2020 · pp. 1–6 Read article
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A New Generalization of Fibonacci Polynomials
Abstract: The Fibonacci sequences, which have an increasing place in scientific studies and are the most wellknown among the number sequences, first appeared in Leonardo Fibonacci's book 'Liber Abaci', which contains many basic problems, in a rabbit problem. Fibonacci sequences were obtained by writing down the monthly total number of new rabbits born by mating only once per month, initially one female and one male rabbit. This sequence, which is obtained …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 8, Issue 2, 2021 · pp. 27–31 Read article
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On Pell Functions and Pell Numbers
Abstract: Number sequences have been studied by many scientists for many years because they find applications in nature and many branches of science. The most well-known number sequence among these integer sequences is the Fibonacci sequence. Later, these integer sequences were generalized and many number sequences were defined and their properties were examined. One of these is Pell number sequences. Pell numbers can be calculated in a way similar to the …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 10, Issue 3, 2023 · pp. 1–9 Read article
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Encoding-Decoding Algorithm Using the Catalan Transform of Weighted Tribonacci Sequence
Abstract: In order to improve information security, this paper presents a unique algorithm for encoding and decoding messages utilizing the Catalan Transform of a Weighted Tribonacci Sequence. Utilizing the Catalan and Tribonacci sequences, the methodology combines the concepts of number theory and combinatorics to create an effective encryption and decryption process. First, an array is created by mapping each character in the plaintext message to its corresponding ASCII value. The ASCII-weighted …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 3, 2024 · pp. 12–16 Read article