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In this article, we explore the determinantal and combinatorial approaches to third-order linear difference equations with variable coefficients. We present and demonstrate some of its properties and we established an explicit formula in terms of the fundamental solutions. Furthermore, as an application, we examine the generalized Jacobsthal sequence and the sequence of powers of two related to the Rogers–Ramanujam type identities establishing new results for some of these polynomial sequences.

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On Solutions of a Third Order Linear Difference Equation with Variable Coefficients. Applications

  • 会议论文

  • 发表日期：

    2025年

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  • Gabriel Freitas Pinheiro,
  • Elen Viviani Pereira Spreafico

摘要

In this article, we explore the determinantal and combinatorial approaches to third-order linear difference equations with variable coefficients. We present and demonstrate some of its properties and we established an explicit formula in terms of the fundamental solutions. Furthermore, as an application, we examine the generalized Jacobsthal sequence and the sequence of powers of two related to the Rogers–Ramanujam type identities establishing new results for some of these polynomial sequences.