{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T04:40:28Z","timestamp":1736138428959,"version":"3.32.0"},"reference-count":17,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,28]],"date-time":"2022-10-28T00:00:00Z","timestamp":1666915200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Council for Scientific and Technological Development\u2014CNPq and the Cear\u00e1 Foundation for Support to Scientific and Technological Development (Funcap)"},{"name":"National Funds through FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["UID\/CED\/00194\/2020"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"There is ongoing research into combinatorial methods and approaches for linear and recurrent sequences. Using the notion of a board defined for the Fibonacci sequence, this work introduces the Padovan sequence combinatorial approach. Thus, mathematical theorems are introduced that refer to the study of the Padovan combinatorial model and some of its extensions, namely Tridovan, Tetradovan and its generalization (Z-dovan). Finally, we obtained a generalization of the Padovan combinatorial model, which was the main result of this research.<\/jats:p>","DOI":"10.3390\/axioms11110598","type":"journal-article","created":{"date-parts":[[2022,10,30]],"date-time":"2022-10-30T03:45:00Z","timestamp":1667101500000},"page":"598","source":"Crossref","is-referenced-by-count":4,"title":["Combinatorial Interpretation of Numbers in the Generalized Padovan Sequence and Some of Its Extensions"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1966-7097","authenticated-orcid":false,"given":"Renata Passos Machado","family":"Vieira","sequence":"first","affiliation":[{"name":"Departament Mathametic, Federal University of Ceara, Campus Fortaleza, Fortaleza 60020-181, Cear\u00e1, Brazil"}]},{"given":"Francisco Regis Vieira","family":"Alves","sequence":"additional","affiliation":[{"name":"Departament Mathametic, Federal Institute of Science and Technology Education of the State of Cear\u00e1, Campus Fortaleza, Fortaleza 62930-000, Cear\u00e1, Brazil"}]},{"given":"Paula Maria Machado Cruz","family":"Catarino","sequence":"additional","affiliation":[{"name":"Departament Mathametic, University of Tr\u00e1s-os-Montes and Alto Douro, 5000-801 Vila Real, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,28]]},"reference":[{"key":"ref_1","unstructured":"Padovan, R. 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Fibonacci and Lucas Numbers with Applications, Springer.","DOI":"10.1002\/9781118742297"},{"key":"ref_14","first-page":"24","article-title":"Propriedades das extens\u00f5es da Sequ\u00eancia de Padovan","volume":"15","author":"Vieira","year":"2019","journal-title":"Rev. Eletron. Paul. CQD"},{"key":"ref_15","first-page":"100","article-title":"Sequ\u00eancia Matricial (s1,s2,s3)-tridovan e propriedades","volume":"16","author":"Vieira","year":"2019","journal-title":"Rev. Eletron. Paul. CQD"},{"key":"ref_16","first-page":"90","article-title":"Matrices which have a similar properties to padovan q-matrix and its generalized relations","volume":"7","author":"Seenukul","year":"2015","journal-title":"Sakon Nakhon Rajabhat Univ. J. Sci. Technol."},{"key":"ref_17","unstructured":"Mehdaoui, A. (2021). Combinatoire des Transversales de la Pyramide de Pascal. [Ph.D. Thesis, University of Sciences and Technology Houari Boumediene]."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/11\/598\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T04:04:48Z","timestamp":1736136288000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/11\/598"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,28]]},"references-count":17,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["axioms11110598"],"URL":"https:\/\/doi.org\/10.3390\/axioms11110598","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,10,28]]}}}