Generalized Pisano numbers
Yueksel Soykan, Inci Okumus, Erkan Tasdemir
article (Uluslararası, Hakemli) | Yazar(lar): Yueksel Soykan, Inci Okumus, Erkan Tasdemir | Yıl: 2022 | Dergi/Kurum: NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS | İndeks: WOS.ESCI | DOI: 10.7546/nntdm.2022.28.3.477-490 | Anahtar Kelimeler: Pisano numbers, Pisano-Lucas numbers, Tribonacci numbers, Modified Oresme nu
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.