Article ID: MTJPAM-D-24-00007

Title: On color palindrome compositions


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-24-00007; Volume 6 / Issue 3 / Year 2024, Pages 269-283

Document Type: Research Paper

Author(s): ‪Busra Al a , Mustafa Alkan b

aDepartment of Computer Technologies and Programming, Manavgat Vocational School, Akdeniz University, Antalya, Turkey

bDepartment of Mathematics, Akdeniz University, Antalya, Turkey

Received: 15 January 2024, Accepted: 25 June 2024, Published: 10 July 2024

Corresponding Author: Busra Al (Email address: busraal@akdeniz.edu.tr)

Full Text: PDF

Abstract

In this paper, we decompose the palindrome composition set of the positive integer to construct an efficient algorithm for obtaining elements. We also develop techniques to investigate generating functions for the numbers of color palindrome compositions with respect to some coloring rules. Then we investigate the generating function, recurrence relations, and Binet formula for the n-color palindrome compositions, and so we see that the sequence of integers corresponding to the n-color palindrome compositions is the combination of even Fibonacci numbers and odd Lucas numbers. We also determine the relationships among color palindrome compositions, and the Fibonacci numbers. Moreover, by using decompositions and algorithms, we make patterns of some color palindrome compositions.

Keywords: Compositions of the positive integers, palindrome compositions, the color palindrome compositions, Binet’s formulas, Fibonacci numbers, Lucas numbers, generating functions

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Cite this article

How to cite this article: B. Al and M. Alkan, On color palindrome compositions, Montes Taurus J. Pure Appl. Math. 6 (3), 269-283, 2024; Article ID: MTJPAM-D-24-00007.