On color palindrome compositions
Montes Taurus Journal of Pure and Applied Mathematics, vol.6, no.3 Special Issue, pp.269-283, 2024 (Scopus)
- Publication Type: Article / Article
- Volume: 6 Issue: 3 Special Issue
- Publication Date: 2024
- Journal Name: Montes Taurus Journal of Pure and Applied Mathematics
- Journal Indexes: Scopus
- Page Numbers: pp.269-283
- Keywords: Binet’s formulas, Compositions of the positive integers, Fibonacci numbers, generating functions, Lucas numbers, palindrome compositions, the color palindrome compositions
- Akdeniz University Affiliated: Yes
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.