Generalized Pisano numbers

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SOYKAN Y., Okumus I., TAŞDEMİR E.

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, vol.28, no.3, pp.477-490, 2022 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.7546/nntdm.2022.28.3.477-490
  • Journal Name: NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.477-490
  • Keywords: Pisano numbers, Pisano-Lucas numbers, Tribonacci numbers, Modified Oresme numbers, Oresme-Lucas numbers, Oresme numbers
  • Istanbul University Affiliated: No

Abstract

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.