On the Study of Bifurcating Right Fibonomial Numbers and Rb-Trinomial Numbers

Fontene ́ once introduced a generalized form of binomial coefficients by substituting natural numbers with terms from an arbitrary sequence Aₙ of real or complex numbers, which he referred to as Fibonomial coefficients. Since then, significant interest has developed around Fibonomial numbers which is two dimensional in which n is divided into two parts, particularly when the sequence Aₙ is chosen as Fₙ, the well-known Fibonacci sequence. More recently, researchers have explored a further extension by considering Aₙ =FₙR, the sequence of right Fibonacci numbers. In this paper, we take this generalization a step further by defining Fibonomial coefficients based on the sequence Aₙ =Fₙ^ (R (a, b) ), known as the right Bifurcating Fibonacci numbers. Also, there were a new generalization was established for three-dimensional Fibonomial numbers which is the extension of n divided into three parts, known as F-trinomial numbers. In this paper, we choose right bifurcating Fibonacci sequence and introduced RB-trinomial numbers. Then, we derive several identities associated with both of them. Additionally, we examine some of their bounds for both numbers. Keywords: Binomial Coefficients, Fibonacci Numbers, Bifurcating Fibonacci numbers, Fibonomial Coefficients, Trinomial Coefficients,