{"id":"https://openalex.org/W4415823664","doi":"https://doi.org/10.3390/axioms14110819","title":"A Grammatical Interpretation of Horadam Sequences","display_name":"A Grammatical Interpretation of Horadam Sequences","publication_year":2025,"publication_date":"2025-11-03","ids":{"openalex":"https://openalex.org/W4415823664","doi":"https://doi.org/10.3390/axioms14110819"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14110819","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110819","pdf_url":"https://www.mdpi.com/2075-1680/14/11/819/pdf?version=1762152267","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/11/819/pdf?version=1762152267","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110343960","display_name":"Jiaoyun Liu","orcid":"https://orcid.org/0000-0001-6661-445X"},"institutions":[{"id":"https://openalex.org/I119203015","display_name":"Shandong University of Technology","ror":"https://ror.org/02mr3ar13","country_code":"CN","type":"education","lineage":["https://openalex.org/I119203015"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jun-Ying Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China"],"raw_orcid":"https://orcid.org/0000-0001-6661-445X","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China","institution_ids":["https://openalex.org/I119203015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104962661","display_name":"Hailing Li","orcid":"https://orcid.org/0000-0002-9903-3683"},"institutions":[{"id":"https://openalex.org/I119203015","display_name":"Shandong University of Technology","ror":"https://ror.org/02mr3ar13","country_code":"CN","type":"education","lineage":["https://openalex.org/I119203015"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hai-Ling Li","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China","institution_ids":["https://openalex.org/I119203015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100419461","display_name":"Zhihong Zhang","orcid":"https://orcid.org/0000-0002-2959-3538"},"institutions":[{"id":"https://openalex.org/I119203015","display_name":"Shandong University of Technology","ror":"https://ror.org/02mr3ar13","country_code":"CN","type":"education","lineage":["https://openalex.org/I119203015"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi-Hong Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China","institution_ids":["https://openalex.org/I119203015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110343960"],"corresponding_institution_ids":["https://openalex.org/I119203015"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.8037,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.77422873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"14","issue":"11","first_page":"819","last_page":"819"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9283000230789185,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9283000230789185,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.04910000041127205,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.002899999963119626,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.7195000052452087},{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.6093000173568726},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6083999872207642},{"id":"https://openalex.org/keywords/grammar","display_name":"Grammar","score":0.5156999826431274},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.34850001335144043}],"concepts":[{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.7195000052452087},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.6093000173568726},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6083999872207642},{"id":"https://openalex.org/C26022165","wikidata":"https://www.wikidata.org/wiki/Q8091","display_name":"Grammar","level":2,"score":0.5156999826431274},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5113000273704529},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41819998621940613},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4016000032424927},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.365200012922287},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.34850001335144043},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.33550000190734863},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30140000581741333},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2913999855518341},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2824999988079071},{"id":"https://openalex.org/C155092808","wikidata":"https://www.wikidata.org/wiki/Q182557","display_name":"Computational linguistics","level":2,"score":0.26820001006126404}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14110819","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110819","pdf_url":"https://www.mdpi.com/2075-1680/14/11/819/pdf?version=1762152267","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4b721c1d2006410b9d743c058eb9e3c8","is_oa":true,"landing_page_url":"https://doaj.org/article/4b721c1d2006410b9d743c058eb9e3c8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 11, p 819 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14110819","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110819","pdf_url":"https://www.mdpi.com/2075-1680/14/11/819/pdf?version=1762152267","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6422227919","display_name":"\u7ec4\u5408\u7edf\u8ba1\u91cf\u4e0e\u6784\u9020\u6027\u7ec4\u5408\u65b9\u6cd5\u7684\u7814\u7a76","funder_award_id":"12071063","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415823664.pdf","grobid_xml":"https://content.openalex.org/works/W4415823664.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W111714761","https://openalex.org/W2061104416","https://openalex.org/W2133208152","https://openalex.org/W2143170067","https://openalex.org/W2333194709","https://openalex.org/W2962915708","https://openalex.org/W2964196775","https://openalex.org/W3177420406","https://openalex.org/W4254246953","https://openalex.org/W4283214826","https://openalex.org/W4303648680","https://openalex.org/W4365505736","https://openalex.org/W4402408230","https://openalex.org/W4404821171","https://openalex.org/W4409369378","https://openalex.org/W4411851894","https://openalex.org/W4412422771"],"related_works":[],"abstract_inverted_index":{"The":[0],"Horadam":[1,28,48],"sequence":[2],"{Hn(a,b;p,q)}n\u2a7e0":[3],"has":[4],"been":[5],"widely":[6],"studied":[7],"in":[8],"combinatorics":[9],"and":[10,51,55,69],"number":[11],"theory.":[12],"In":[13],"this":[14,31],"paper,":[15],"we":[16,33,41],"find":[17],"that":[18],"the":[19,43,67,75],"context-free":[20],"grammar":[21],"G={x\u2192px+y,y\u2192qx}":[22],"can":[23,63],"be":[24,64],"used":[25],"to":[26,59],"generate":[27],"sequences.":[29],"Using":[30],"grammar,":[32],"deduce":[34],"several":[35],"identities,":[36,61],"including":[37],"Cassini-like":[38],"identities.":[39],"Moreover,":[40],"investigate":[42],"relationship":[44],"between":[45],"two":[46,76],"distinct":[47],"sequences":[49,71],"Hn(a,b;p,q)":[50],"Hn(c,d;p,q)":[52],"with":[53],"(a,b)\u2260(c,d)":[54],"provide":[56],"an":[57],"approach":[58],"derive":[60],"which":[62],"illustrated":[65],"by":[66],"Fibonacci":[68],"Lucas":[70],"as":[72,74],"well":[73],"kinds":[77],"of":[78],"Chebyshev":[79],"polynomials.":[80]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-11-03T00:00:00"}
