@article{article_1406328, title={On unrestricted dual-generalized complex Horadam numbers}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={73}, pages={517–528}, year={2024}, DOI={10.31801/cfsuasmas.1406328}, author={Ait-amrane, Nacima Rosa and Tan, Elif}, keywords={Hypercomplex numbers, dual generalized complex numbers, Horadam numbers, Fibonacci numbers}, abstract={This research introduces a novel category of dual-generalized complex numbers, with components represented by unrestricted Horadam numbers. We present various recurrence relations, summation formulas, the Binet formula, and the generating function associated with these numbers. Additionally, a comprehensive bilinear index-reduction formula is derived, which encompasses Vajda’s, Catalan’s, Cassini’s, D’Ocagne’s, and Halton’s identities as specific cases.}, number={2}, publisher={Ankara University}