{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:14:08Z","timestamp":1760058848997,"version":"build-2065373602"},"reference-count":66,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,7]],"date-time":"2025-05-07T00:00:00Z","timestamp":1746576000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Young and Middle-Aged Key Teachers Project of Zhoukou Normal University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Six well-known sequences (Fibonacci and Lucas numbers, Pell and Pell\u2013Lucas polynomials, and Chebyshev polynomials) are characterized by quadratic linear recurrence relations. They are unified and reviewed under a common framework. Several useful properties (such as Binet-form expressions, Cassini identities, and Catalan formulae) and remarkable results concerning power sums, ordinary convolutions, and binomial convolutions are presented by employing the symmetric feature, series rearrangements, and the generating function approach. Most of the classical results concerning these six number\/polynomial sequences are recorded as consequences.<\/jats:p>","DOI":"10.3390\/sym17050714","type":"journal-article","created":{"date-parts":[[2025,5,7]],"date-time":"2025-05-07T08:20:53Z","timestamp":1746606053000},"page":"714","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Overview of Six Number\/Polynomial Sequences Defined by Quadratic Recurrence Relations"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-1779-0372","authenticated-orcid":false,"given":"Yujie","family":"Kang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1972-4482","authenticated-orcid":false,"given":"Marta Na","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8425-212X","authenticated-orcid":false,"given":"Wenchang","family":"Chu","sequence":"additional","affiliation":[{"name":"Independent Researcher, Via Dalmazio Birago 9\/E, 73100 Lecce, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Levy, H., and Lessman, F. 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