Recurrence sequences with exponential input terms arise naturally in symbolic recurrence theory and extend classical families such as Fibonacci and Lucas. In earlier work, we established a general theorem that provides explicit iterative formulas for computing particular solutions of generalized Leonardo-type recurrences. The present article focuses on concrete applications of that result. We derive and present explicit particular solutions for the special cases of orders m = 1, 2, 3, 4, 5, 6 illustrating how the general framework specializes to low-order recurrences. These examples highlight the role of characteristic polynomials, root multiplicities, and resonance phenomena, while offering closed-form constructions that bridge classical recurrence identities with modern symbolic methods.
Y ksel Soykan (Mon,) studied this question.