In the present paper, for a positive integer $r$, we study bi-periodic $r$-Fibonacci sequence and its family of companion sequences, bi-periodic $r$-Lucas sequence of type $s$ with $1 \leq s \leq r$, which extend the classical Fibonacci and Lucas sequences. Afterwards, we establish the link between the bi-periodic $r$-Fibonacci sequence and its companion sequences. Furthermore, we give their properties as linear recurrence relations, generating functions, explicit formulas and Binet forms.
bi-periodic r-Fibonacci sequence bi-periodic r-Lucas sequence companion sequence recurrence relation generating function explicit formula Binet form
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Yayımlanma Tarihi | 1 Haziran 2022 |
Yayımlandığı Sayı | Yıl 2022 Cilt: 51 Sayı: 3 |