Hybrid numbers with balancing and Lucas balancing hybrid number coefficients

Year 2025, Volume: 74 Issue: 3, 395 - 402, 23.09.2025

Murat Turan , Sıddıka Özkaldı Karakuş

https://doi.org/10.31801/cfsuasmas.1561936

Abstract

In this note, we made a connection between hybrid numbers and hybrid balancing, and hybrid Lucas balancing number. Initially, we obtained for these new number recurrence relation, some important relations among new numbers, and Binet's like formula. Afterwards, using Binet's like formula, we obtained some identities such as D'ocagne's identity, Honsberger identity, Catalan identity, and Cassini identity.

Keywords

Hybrid numbers , balancing numbers , Lucas numbers

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