On Tricomplex Horadam Numbers: A New Class of Horadam Sequences

This study introduces an innovative approach to Horadam sequences. The aim of this paper is to investigate the Tricomplex Horadam sequence and its properties. It begins with the tricomplex ring T and key results related to Horadam-type sequences. The Tricomplex Horadam sequence is then defined, with a discussion of its properties, the Binet formula, and the generating function in vector form. Next, several fundamental identities, including the Tagiuri–Vajda and d’Ocagne identities, are examined, along with their implications and examples from previous Tricomplex Horadam-type sequences. Finally, the sum of terms associated with the Tricomplex Horadam sequence is presented. The research problem consists in determining properties symmetrical or analogous to the Horadam-type sequence for the Tricomplex Horadam sequence.