September 12, 2025

Left Bifurcating Fibonomial Numbers and LB-Trinomial Numbers

Key Points

This paper introduces LB-trinomial numbers related to left bifurcating fibonacci numbers, expanding on earlier studies.
It derives new identities for LB-trinomial numbers, offering insights into their mathematical relationships.
The exploration includes bounds for these numbers, contributing to a deeper understanding of their properties.
The study builds on prior research on fibonomial coefficients and various forms of fibonacci numbers.

Abstract

Fontené first generalized binomial coefficients in 1915 by using terms of an arbitrary sequence, giving rise to Fibonomial coefficients. Later, these were studied with Fibonacci numbers and then with left Fibonacci numbers. In this paper, we extend the idea further using left bifurcating Fibonacci numbers. With this sequence, we introduce LB-trinomial numbers and derive related identities. We also investigate some bounds for these new numbers.

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