Generalized Pisano numbers

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SOYKAN Y., Okumus I., TAŞDEMİR E.

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, cilt.28, sa.3, ss.477-490, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 28 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.7546/nntdm.2022.28.3.477-490
  • Dergi Adı: NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.477-490
  • Anahtar Kelimeler: Pisano numbers, Pisano-Lucas numbers, Tribonacci numbers, Modified Oresme numbers, Oresme-Lucas numbers, Oresme numbers
  • İstanbul Üniversitesi Adresli: Hayır

Özet

In this paper, we define and investigate the generalized Pisano sequences and we deal with, in detail, two special cases, namely, Pisano and Pisano-Lucas sequences. We present Binet's formulas, generating functions and Simson's formulas for these sequences. Moreover, we give some identities and matrices associated with these sequences. Furthermore, we show that there are close relations between Pisano and Pisano-Lucas numbers and modified Oresme, Oresme-Lucas and Oresme numbers.