Asian Research Journal of Mathematics

This paper introduces the framework of generalized hyperbolic Pandita numbers constructed over the bidimensional Clifford algebra of hyperbolic numbers, contributing a novel class of structured sequences to the expanding domain of number theory. Anchored in the principles of hyperbolic systems, these constructs pave the way for exploring algebraic symmetries and recursive behaviors beyond classical formulations. Special attention is devoted to notable cases, including the hyperbolic Pandita and hyperbolic Pandita-Lucas numbers, whose properties are meticulously examined. To deepen understanding and facilitate computation, we derive explicit closed-form representations using Binet-type formulas, construct generating functions through formal power series, and establish summation expressions with broad applicability. Additionally, matrix-based representations are developed to offer an algebraic lens through which structural dynamics can be modeled and analyzed. These formulations not only enrich the theoretical foundations of discrete mathematics and symbolic computation but also highlight promising applications in engineering disciplines— particularly in the modeling of iterative systems, signal transformations, the analysis of complex networks, and cryptographic systems. The insights presented herein lay the groundwork for future exploration into hybrid sequence systems and their role in interdisciplinary problem solving.