On color palindrome compositions

AL B., ALKAN M.

Montes Taurus Journal of Pure and Applied Mathematics, cilt.6, sa.3 Special Issue, ss.269-283, 2024 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6 Sayı: 3 Special Issue
  • Basım Tarihi: 2024
  • Dergi Adı: Montes Taurus Journal of Pure and Applied Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.269-283
  • Anahtar Kelimeler: Binet’s formulas, Compositions of the positive integers, Fibonacci numbers, generating functions, Lucas numbers, palindrome compositions, the color palindrome compositions
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.