{"id":"https://openalex.org/W4394840243","doi":"https://doi.org/10.1155/2024/9352986","title":"On the Leonardo Sequence via Pascal-Type Triangles","display_name":"On the Leonardo Sequence via Pascal-Type Triangles","publication_year":2024,"publication_date":"2024-04-16","ids":{"openalex":"https://openalex.org/W4394840243","doi":"https://doi.org/10.1155/2024/9352986"},"language":"en","primary_location":{"id":"doi:10.1155/2024/9352986","doi":"https://doi.org/10.1155/2024/9352986","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2024/9352986","pdf_url":"https://downloads.hindawi.com/journals/jmath/2024/9352986.pdf","source":{"id":"https://openalex.org/S2764668616","display_name":"Journal of Mathematics","issn_l":"2314-4629","issn":["2314-4629","2314-4785"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jmath/2024/9352986.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020562878","display_name":"Serpil Hal\u0131c\u0131","orcid":"https://orcid.org/0000-0002-8071-0437","observed_orcids":["https://orcid.org/0000-0002-8071-0437"]},"institutions":[{"id":"https://openalex.org/I48843708","display_name":"Pamukkale University","ror":"https://ror.org/01etz1309","country_code":"TR","type":"education","lineage":["https://openalex.org/I48843708"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Serpil Hal\u0131c\u0131","raw_affiliation_strings":["Department of Mathematics, Pamukkale Uni., Denizli 20160, T\u00fcrkiye"],"raw_orcid":"https://orcid.org/0000-0002-8071-0437","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pamukkale Uni., Denizli 20160, T\u00fcrkiye","institution_ids":["https://openalex.org/I48843708"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042907104","display_name":"\u015eule \u00c7\u00fcr\u00fck","orcid":"https://orcid.org/0000-0002-4514-6156","observed_orcids":["https://orcid.org/0000-0002-4514-6156"]},"institutions":[{"id":"https://openalex.org/I48843708","display_name":"Pamukkale University","ror":"https://ror.org/01etz1309","country_code":"TR","type":"education","lineage":["https://openalex.org/I48843708"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Sule Curuk","raw_affiliation_strings":["Department of Mathematics, Pamukkale Uni., Denizli 20160, T\u00fcrkiye"],"raw_orcid":"https://orcid.org/0000-0002-4514-6156","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pamukkale Uni., Denizli 20160, T\u00fcrkiye","institution_ids":["https://openalex.org/I48843708"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5020562878"],"corresponding_institution_ids":["https://openalex.org/I48843708"],"apc_list":{"value":2060,"currency":"USD","value_usd":2060},"apc_paid":{"value":2060,"currency":"USD","value_usd":2060},"fwci":0.2306,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.32928862,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"2024","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.975600004196167,"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":0.975600004196167,"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":0.016499999910593033,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.0017999999690800905,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bicomplex-numbers","display_name":"bicomplex numbers","score":0.9929999709129333},{"id":"https://openalex.org/keywords/fibonacci-sequence","display_name":"Fibonacci numbers","score":0.828000009059906},{"id":"https://openalex.org/keywords/number-sequences","display_name":"number sequences","score":0.550000011920929},{"id":"https://openalex.org/keywords/combinatorial-identities","display_name":"combinatorial identities","score":0.8230000138282776}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.9348307847976685},{"id":"https://openalex.org/C75608658","wikidata":"https://www.wikidata.org/wiki/Q44395","display_name":"Pascal (unit)","level":2,"score":0.8632799983024597},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7978957891464233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7709944248199463},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5464807748794556},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5348300933837891},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.37357181310653687},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1250268816947937},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.049367547035217285},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2024/9352986","doi":"https://doi.org/10.1155/2024/9352986","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2024/9352986","pdf_url":"https://downloads.hindawi.com/journals/jmath/2024/9352986.pdf","source":{"id":"https://openalex.org/S2764668616","display_name":"Journal of Mathematics","issn_l":"2314-4629","issn":["2314-4629","2314-4785"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jjmath:9352986","doi":null,"is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/jmath/2024/9352986.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:4d27ff95d5994d74a93485dbe9d00d14","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/4d27ff95d5994d74a93485dbe9d00d14","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,"listed_in":[],"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":"Journal of Mathematics, Vol 2024 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2024/9352986","doi":"https://doi.org/10.1155/2024/9352986","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2024/9352986","pdf_url":"https://downloads.hindawi.com/journals/jmath/2024/9352986.pdf","source":{"id":"https://openalex.org/S2764668616","display_name":"Journal of Mathematics","issn_l":"2314-4629","issn":["2314-4629","2314-4785"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4394840243.pdf","grobid_xml":"https://content.openalex.org/works/W4394840243.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W2168834368","https://openalex.org/W2898047947","https://openalex.org/W2922150288","https://openalex.org/W2978732923","https://openalex.org/W2978936635","https://openalex.org/W3170600856","https://openalex.org/W3211573839","https://openalex.org/W4288515263","https://openalex.org/W4294285687","https://openalex.org/W4311623772","https://openalex.org/W4322488590","https://openalex.org/W4353091686","https://openalex.org/W4380153723"],"related_works":["https://openalex.org/W4414099580","https://openalex.org/W4312141688","https://openalex.org/W4381712798","https://openalex.org/W7204900073","https://openalex.org/W4389047039","https://openalex.org/W4200316951","https://openalex.org/W7130505471","https://openalex.org/W4393303228","https://openalex.org/W3170600856","https://openalex.org/W7002468942"],"abstract_inverted_index":{"In":[0],"this":[1,44,73,95,99],"study,":[2,45],"we":[3,46,68],"discussed":[4],"the":[5,30,37,40,52,61,64,70,78,88,92],"Leonardo":[6,56],"number":[7,49],"sequence,":[8],"which":[9],"has":[10],"been":[11],"studied":[12],"recently":[13],"and":[14,21],"caught":[15],"more":[16],"attention.":[17],"We":[18,81],"used":[19],"Pascal":[20],"Hosoya-like":[22],"triangles":[23],"to":[24,28],"make":[25],"it":[26],"easier":[27],"examine":[29],"basic":[31],"properties":[32,41],"of":[33,39,55,72,94],"these":[34],"numbers.":[35,66],"With":[36],"help":[38],"obtained":[42],"in":[43,87,98],"defined":[47,75],"a":[48],"sequence":[50,76,96],"containing":[51],"new":[53],"type":[54],"numbers":[57],"created":[58],"by":[59,91],"choosing":[60],"coefficients":[62],"from":[63],"bicomplex":[65],"Furthermore,":[67],"gave":[69],"relationship":[71],"newly":[74],"with":[77],"Fibonacci":[79],"sequence.":[80],"also":[82],"provided":[83,90],"some":[84],"important":[85],"identities":[86],"literature":[89],"elements":[93],"described":[97],"paper.":[100]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2024-04-17T00:00:00"}
