Bi-periodic incomplete Lucas numbers

Abstract

In this paper, by presenting bi-periodic Lucas numbers as a binomial sum, we introduce the bi-periodic incomplete Lucas numbers. After that, by using the bi-periodic incomplete Lucas numbers, we derive the recurrence relation and the generating function of these numbers as well as investigated some properties over them. Additionally, as another main result of this paper, we give some relations between bi-periodic incomplete Lucas numbers and bi-periodic incomplete Fibonacci numbers.