Products of General Fibonomial Coefficients via Matrices

Abstract

As a sequential analogue of binomial coefficients, we consider general Fibonomial coefficients with indices in arithmetic progressions. We give a recurrence relation and a generating matrix for the products of these coefficients. We find explicitly the spectrum of the generating matrix by constructing new relationships between the coefficients and characteristic polynomials of general Pascal matrices. We derive various identities for the general Fibonomial coefficients. Finally, we present a matrix approach to derive a formula for sums of these coefficients. © 2025 Elsevier B.V., All rights reserved.