**Title:** On generalizations of Tribonacci numbers

**Montes Taurus J. Pure Appl. Math.** / ISSN: 2687-4814

**Article ID:** MTJPAM-D-21-00076; **Volume 4 / Issue 1 / Year 2022**, Pages 135-141

**Document Type:** Research Paper

**Author(s):** Ortaç Öneş ^{a} , Mustafa Alkan ^{b}

^{a}Akdeniz University, Department of Mathematics, Antalya 07058, Turkey

^{b}Akdeniz University, Department of Mathematics, Antalya 07058, Turkey

Received: 17 December 2021, Accepted: 7 January 2022, Published: 9 February 2022.

** Corresponding Author:** Ortaç Öneş (Email address: ortacns@akdeniz.edu.tr)

**Full Text:** PDF

**Abstract**

In this article, some generalizations of the results in the literature are obtained by using the sequences over an integral domain with the help of matrix method. Then some generalizations for the d’Ocagne identity, the Honsberger’s formula, the Cassini’s identity, the Catalan’s identity are given. Finally, Binet formulas of sequences in the literature are unified in a theorem.

**Keywords:** Integral domain, Tribonacci numbers, Tribonacci sequences

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