New families of Horadam numbers associated with finite operators and their applications
Can Kizilates
article (Uluslararası, Hakemli) | Yazar(lar): Can Kizilates | Yıl: 2021 | Dergi/Kurum: MATHEMATICAL METHODS IN THE APPLIED SCIENCES | İndeks: WOS.SCI | DOI: 10.1002/mma.7702 | Anahtar Kelimeler: closed formula, finite operator, generating function, Horadam numbers, tridiagonal determinant — Özet: In this paper, by appl
In this paper, by applying finite operator to the Horadam sequence, we define the Horadam finite operator sequences. We not only give some special cases of this new sequences but also investigate some properties of our new sequences such as recurrent relation, Binet-like formula, summation formula, and generating function, respectively. We also present closed formula for the Horadam finite operator numbers and their special cases in terms of tridiagonal determinants. Moreover, by using the tridiagonal determinant, we once again verify the recurrence relation of the Horadam finite operator numbers.