<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we bring into light, study the polygonal structure of Fibonacci polynomials that are placed clockwise on these by a number corresponding to each vertex. Also, we find the relation between the numbers with such vertices. We present a relation for obtained sequence in an <italic>n</italic>-gon yielding the <italic>m</italic>-th term formed at <italic>k</italic> vertices. Also, we apply these situations to Lucas polynomials and find new recurrence relations. Then, the numbers obtained by writing the coefficients of these polynomials in step form are shown in OEIS.</p>
</abstract>

In this paper, we bring into light, study the polygonal structure of Fibonacci polynomials that are placed clockwise on these by a number corresponding to each vertex. Also, we find the relation between the numbers with such vertices. We present a relation for obtained sequence in an n-gon yielding the m-th term formed at k vertices. Also, we apply these situations to Lucas polynomials and find new recurrence relations. Then, the numbers obtained by writing the coefficients of these polynomials in step form are shown in OEIS.

Fibonacci and Lucas Polynomials in <italic>n</italic>-gon

Department of Mathematics and Computer Science

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":{"italic":"n","content":["Fibonacci and Lucas Polynomials in","-gon"]}}

In this paper, we bring into light, study the polygonal structure of Fibonacci polynomials that are placed clockwise on these by a number corresponding to each...

Fibonacci and Lucas Polynomials in n-gon

Published Online: Mar 27, 2023

Page range: 127 - 140

Received: Aug 23, 2022

Accepted: Dec 22, 2022

DOI: https://doi.org/10.2478/auom-2023-0023

Keywords
Binet formula, Lucas polynomials, Fibonacci polynomials, Recurrence relation

© 2023 Bahar Kuloğlu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Fibonacci and Lucas Polynomials in n-gon

Published Online: Mar 27, 2023

Page range: 127 - 140

Received: Aug 23, 2022

Accepted: Dec 22, 2022

DOI: https://doi.org/10.2478/auom-2023-0023

KeywordsBinet formula, Lucas polynomials, Fibonacci polynomials, Recurrence relation

© 2023 Bahar Kuloğlu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Binet formula, Lucas polynomials, Fibonacci polynomials, Recurrence relation