{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T00:27:21Z","timestamp":1759364841131,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T00:00:00Z","timestamp":1759104000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Mathematics Centre of the University of Minho","award":["UID\/00013"],"award-info":[{"award-number":["UID\/00013"]}]},{"DOI":"10.13039\/100030712","name":"Federal University of Tocantins","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100030712","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Symmetry"],"abstract":"<jats:p>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\u2013Vajda and d\u2019Ocagne 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.<\/jats:p>","DOI":"10.3390\/sym17101616","type":"journal-article","created":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:59:46Z","timestamp":1759150786000},"page":"1616","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Tricomplex Horadam Numbers: A New Class of Horadam Sequences"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5221-6087","authenticated-orcid":false,"given":"Douglas C.","family":"Santos","sequence":"first","affiliation":[{"name":"Education Department of the State of Bahia, Barreiras 41745-004, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6917-5093","authenticated-orcid":false,"given":"Paula M. M. C.","family":"Catarino","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Tr\u00e1s-os-Montes and Alto Douro, 5000-801 Vila Real, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6684-9961","authenticated-orcid":false,"given":"Eudes A.","family":"Costa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Federal University of Tocantins, Arraias 77330-000, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1080\/00029890.1961.11989696","article-title":"A generalized Fibonacci sequence","volume":"68","author":"Horadam","year":"1961","journal-title":"Am. Math. 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