Incomplete Tribonacci–Lucas Numbers and Polynomials

Abstract

In this paper, we define Tribonacci-Lucas polynomials and present Tribonacci-Lucas numbers and polynomials as a binomial sum. Then, we introduce incomplete Tribonacci-Lucas numbers and polynomials. In addition we derive recurrence relations, some properties and generating functions of these numbers and polynomials. Also, we find the generating function of incomplete Tribonacci polynomials which is given as the open problem in [12].

Tribonacci Sayıları ile İlişkili Bir Tamsayı Dizisininin Genellemesi

“…Together with these and using (8) we get the coefficients of 𝑡 2𝑛 which gives the exact formula for the polynomial sequence…”

“…There are many studies about Tribonacci polynomials. You can see [4][5][6][7][8][9] for the studies. In 1973 Tribonacci polynomial sequence (𝑇 𝑛 ( 𝑥 ) )was defined by Hoggatt and Bicknell in [3].…”

Generating Functions of Binary Products of Tribonacci and Tribonacci Lucas Polynomials and Special Numbers

“…(1.3) Also, in [24], authors defined Tribonacci Lucas polynomials, incomplete Tribonacci Lucas numbers and incomplete Tribonacci Lucas polynomials. That is, Tribonacci Lucas polynomials are defined by…”

Incomplete k-Pell, k-Pell-Lucas and Modified k-Pell Numbers

“…For example, the mathematical term incomplete on Fibonacci, Lucas and Tribonacci numbers and polynomials has been considered. For studies about the incomplete Fibonacci and Lucas numbers and their generating functions and properties, see, for example, [15] and [24], and for the incomplete Tribonacci numbers, see, for example, [26] and [33]. The incomplete generalized Fibonacci and Lucas numbers are presented in [10] and the incomplete generalized Jacobsthal and Jacobsthal-Lucas numbers in [11].…”

“…The incomplete generalized Fibonacci and Lucas numbers are presented in [10] and the incomplete generalized Jacobsthal and Jacobsthal-Lucas numbers in [11]. We may also refer to [25], [28], [29] and [34], among others.…”