{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T02:15:17Z","timestamp":1767665717461},"reference-count":0,"publisher":"National Library of Serbia","issue":"4","license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/publicdomain\/zero\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Filomat"],"published-print":{"date-parts":[[2021]]},"abstract":"<jats:p>Special integers sequences have been the center of attention for many\n   researchers, as well as the sequences of quaternions where its components\n   are the elements of these sequences. Motivated by a rational sequence, we\n   consider the quaternions with components Vietoris? numbers and investigate\n   some of its properties. For this sequence a two and three term recurrence\n   relation is established, as well as a Binet?s type formula. Moreover the\n   generating function for this sequence is introduced and also the determinant\n   of some tridiagonal matrices are used in order to find elements of this\n   sequence.<\/jats:p>","DOI":"10.2298\/fil2104065c","type":"journal-article","created":{"date-parts":[[2021,11,19]],"date-time":"2021-11-19T09:32:16Z","timestamp":1637314336000},"page":"1065-1086","source":"Crossref","is-referenced-by-count":8,"title":["On a quaternionic sequence with Vietoris\u2019 numbers"],"prefix":"10.2298","volume":"35","author":[{"given":"P.","family":"Catarino","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Tr\u00b4as-os-Montes e Alto Douro, UTAD, Vila Real, Portugal"}]},{"suffix":"R.","given":"Almeida","family":"de","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Tr\u00b4as-os-Montes e Alto Douro, UTAD, Vila Real, Portugal"}]}],"member":"1078","container-title":["Filomat"],"original-title":[],"language":"en","deposited":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T08:16:24Z","timestamp":1685348184000},"score":1,"resource":{"primary":{"URL":"https:\/\/doiserbia.nb.rs\/Article.aspx?ID=0354-51802104065C"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021]]}},"URL":"https:\/\/doi.org\/10.2298\/fil2104065c","relation":{},"ISSN":["0354-5180","2406-0933"],"issn-type":[{"value":"0354-5180","type":"print"},{"value":"2406-0933","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021]]}}}