{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T08:58:09Z","timestamp":1777366689929,"version":"3.51.4"},"reference-count":19,"publisher":"Walter de Gruyter GmbH","issue":"3","license":[{"start":{"date-parts":[[2016,11,1]],"date-time":"2016-11-01T00:00:00Z","timestamp":1477958400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,11,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    In this paper we introduce a generalized Jacobsthal and Jacobsthal-Lucas polynomials, J\n                    <jats:sub>h,n<\/jats:sub>\n                    and j\n                    <jats:sub>h,n<\/jats:sub>\n                    , respectively, that consist on an extension of Jacobsthal's polynomials J\n                    <jats:sub>n<\/jats:sub>\n                    (\ud835\udc65) and Jacobsthal-Lucas polynomials j\n                    <jats:sub>n<\/jats:sub>\n                    (\ud835\udc65). We provide their properties and a generalization of the usual identities. We also present, for each one of these generalized polynomials, their ordinary generating functions and matrices. In the last part of the paper, we present some special kind of tridiagonal matrices whose entries are elements of these generalized polynomials.\n                  <\/jats:p>","DOI":"10.1515\/auom-2016-0048","type":"journal-article","created":{"date-parts":[[2017,9,21]],"date-time":"2017-09-21T06:00:47Z","timestamp":1505973647000},"page":"61-78","source":"Crossref","is-referenced-by-count":3,"title":["On Generalized Jacobsthal and Jacobsthal-Lucas polynomials"],"prefix":"10.2478","volume":"24","author":[{"given":"Paula","family":"Catarino","sequence":"first","affiliation":[{"name":"Mathematics Centre CMAT, Pole CMAT-UTAD, Department of Mathematics, University of Tr\u00e1s-os-Montes e Alto Douro, UTAD, Quinta de Prados 5000-801, Vila Real , Portugal"}]},{"given":"Maria Luisa","family":"Morgado","sequence":"additional","affiliation":[{"name":"Mathematics Centre CMAT, Pole CMAT-UTAD, Department of Mathematics, University of Tr\u00e1s-os-Montes e Alto Douro, UTAD, Quinta de Prados 5000-801, Vila Real , Portugal"}]}],"member":"374","published-online":{"date-parts":[[2017,9,21]]},"reference":[{"key":"2026042716212638707_j_auom-2016-0048_ref_001_w2aab3b7b3b1b6b1ab1ab1Aa","unstructured":"[1] C. 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