K-Narayana sequence self-Similarity. flip graph views of k-Narayana self-Similarity

Özkan, Engi̇n; Kuloğlu, Bahar; Peters, James F.

doi:10.1016/j.chaos.2021.111473

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Introduction3

Some Identities Of New Narayana Triangle1

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2021

2024

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Cited by 8 publications

(4 citation statements)

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“…The properties of various configurations within the triangle array for the Fibonacci triangle were investigated in [4]. In this section, we examine similar properties for the Narayana triangle.…”

Section: Some Identities Of New Narayana Trianglementioning

confidence: 99%

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New Narayana Triangle

Kuloğlu

Özkan

2022

J. Sci. Arts

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Section: Some Identities Of New Narayana Trianglementioning

confidence: 99%

“…(2) where (3) The Narayana numbers and their properties have been studied by Özkan, Ramirez, Petersen, et al [3][4][5][6][7][8][9][10]. In particular, Petersen [5] places them in the Euler-Macmahon-Carlitz/Riordan combinatorial spectrum.…”

Section: Introductionmentioning

confidence: 99%

New Narayana Triangle

Kuloğlu

Özkan

2022

J. Sci. Arts

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“…For other generalizations of the Fibonacci sequence see for example [2,3,4,23,8,30,29,18,19,25,28,14,5].…”

Section: Introductionmentioning

confidence: 99%

On Doubled and Quadrupled Fibonacci Type Sequences

Yilmaz,

Włoch,

Özkan

et al. 2023

Annales Mathematicae Silesianae

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In this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled Narayana’s sequence. We give a binomial direct formula for these sequences using graph methods, and also we derive a number of identities. Moreover, we study matrix generators of these sequences and determine connections with the Pascal’s triangle.

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“…In recent years, many interesting papers investigating the properties of Narayana numbers and Narayana polynomials have been published, see e.g. [8,12,15,16,18].…”

Section: Introductionmentioning

confidence: 99%