Fibonacci and Lucas Polynomials in n-gon

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Kuloǧlu B., ÖZKAN E., Marin M.

Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, cilt.31, sa.2, ss.127-140, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 31 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.2478/auom-2023-0023
  • Dergi Adı: Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.127-140
  • Anahtar Kelimeler: Binet formula, Fibonacci polynomials, Lucas polynomials, Recurrence relation
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

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.