{"id":"https://openalex.org/W4408512147","doi":"https://doi.org/10.1093/jigpal/jzaf005","title":"Generalised Leonardo numbers","display_name":"Generalised Leonardo numbers","publication_year":2025,"publication_date":"2025-02-05","ids":{"openalex":"https://openalex.org/W4408512147","doi":"https://doi.org/10.1093/jigpal/jzaf005"},"language":"en","primary_location":{"id":"doi:10.1093/jigpal/jzaf005","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzaf005","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034083521","display_name":"Carlos M. da Fonseca","orcid":"https://orcid.org/0000-0001-7742-4416"},"institutions":[{"id":"https://openalex.org/I136040515","display_name":"Universidad de Deusto","ror":"https://ror.org/00ne6sr39","country_code":"ES","type":"education","lineage":["https://openalex.org/I136040515"]},{"id":"https://openalex.org/I31151848","display_name":"Technical University of Sofia","ror":"https://ror.org/052prhs50","country_code":"BG","type":"education","lineage":["https://openalex.org/I31151848"]},{"id":"https://openalex.org/I4210111408","display_name":"Kuwait College of Science and Technology","ror":"https://ror.org/01vjvsj67","country_code":"KW","type":"education","lineage":["https://openalex.org/I4210111408"]}],"countries":["BG","ES","KW"],"is_corresponding":false,"raw_author_name":"Carlos M da Fonseca","raw_affiliation_strings":["Kuwait College of Science and Technology , Doha District, Safat 13133, Kuwait; Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Kliment Ohridski Blvd. 8, 1000 Sofia, Bulgaria; University of Deusto, 48007 Bilbao, Spain","Kuwait College of Science and Technology, Doha District, Safat 13133, Kuwait","University of Deusto, 48007 Bilbao, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kuwait College of Science and Technology , Doha District, Safat 13133, Kuwait; Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Kliment Ohridski Blvd. 8, 1000 Sofia, Bulgaria; University of Deusto, 48007 Bilbao, Spain","institution_ids":["https://openalex.org/I4210111408","https://openalex.org/I136040515","https://openalex.org/I31151848"]},{"raw_affiliation_string":"Kuwait College of Science and Technology, Doha District, Safat 13133, Kuwait","institution_ids":["https://openalex.org/I4210111408"]},{"raw_affiliation_string":"University of Deusto, 48007 Bilbao, Spain","institution_ids":["https://openalex.org/I136040515"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018343835","display_name":"Can K\u0131z\u0131late\u015f","orcid":"https://orcid.org/0000-0002-7958-4226"},"institutions":[{"id":"https://openalex.org/I3017902709","display_name":"Zonguldak B\u00fclent Ecevit University","ror":"https://ror.org/01dvabv26","country_code":"TR","type":"education","lineage":["https://openalex.org/I3017902709"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Can K\u0131z\u0131late\u015f","raw_affiliation_strings":["Department of Mathematics , Zonguldak B\u00fclent Ecev\u0131t University, Zonguldak, 67100, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Zonguldak B\u00fclent Ecev\u0131t University, Zonguldak, 67100, Turkey","institution_ids":["https://openalex.org/I3017902709"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085479589","display_name":"Paulo Saraiva","orcid":"https://orcid.org/0000-0002-2856-5033"},"institutions":[{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Paulo Saraiva","raw_affiliation_strings":["Faculty of Economics , University of Coimbra, Av. Dias da Silva, 165, 3004-512 Coimbra, Portugal; CMUC, Department of Mathematics, University of Coimbra, 3000-143 Coimbra, Portugal; CeBER-Centre for Business and Economics Research, Av. Dias da Silva 165, 3004-512 Coimbra, Portugal","CMUC, Department of Mathematics, University of Coimbra, 3000-143 Coimbra, Portugal","Faculty of Economics, University of Coimbra, Av. Dias da Silva, 165, 3004-512 Coimbra, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Economics , University of Coimbra, Av. Dias da Silva, 165, 3004-512 Coimbra, Portugal; CMUC, Department of Mathematics, University of Coimbra, 3000-143 Coimbra, Portugal; CeBER-Centre for Business and Economics Research, Av. Dias da Silva 165, 3004-512 Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]},{"raw_affiliation_string":"CMUC, Department of Mathematics, University of Coimbra, 3000-143 Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]},{"raw_affiliation_string":"Faculty of Economics, University of Coimbra, Av. Dias da Silva, 165, 3004-512 Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064228962","display_name":"A. G. Shannon","orcid":"https://orcid.org/0000-0003-0116-0666"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Anthony G Shannon","raw_affiliation_strings":["Warrane College , University of New South Wales, Kensington NSW 2033, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Warrane College , University of New South Wales, Kensington NSW 2033, Australia","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":6,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":3.3183,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.91211919,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"33","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9975000023841858,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/sequence","display_name":"Sequence (biology)","score":0.7150067090988159},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.6583104133605957},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4416457414627075},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.17538699507713318}],"concepts":[{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7150067090988159},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.6583104133605957},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4416457414627075},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.17538699507713318},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/jigpal/jzaf005","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzaf005","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W188777240","https://openalex.org/W196165080","https://openalex.org/W1971832285","https://openalex.org/W1996905328","https://openalex.org/W2023171532","https://openalex.org/W2051429867","https://openalex.org/W2075646121","https://openalex.org/W2091391788","https://openalex.org/W2140485158","https://openalex.org/W2182274314","https://openalex.org/W2184537627","https://openalex.org/W2312841439","https://openalex.org/W2328961298","https://openalex.org/W2580036407","https://openalex.org/W2978732923","https://openalex.org/W4212795002","https://openalex.org/W4289517769","https://openalex.org/W4311623772","https://openalex.org/W4365450769","https://openalex.org/W4387332574","https://openalex.org/W4389047039","https://openalex.org/W4399783332","https://openalex.org/W4402633928","https://openalex.org/W4402831341","https://openalex.org/W4402831558","https://openalex.org/W4402831655","https://openalex.org/W4402914266","https://openalex.org/W4402914286","https://openalex.org/W4402917423","https://openalex.org/W4403205973","https://openalex.org/W4403207723","https://openalex.org/W4403297216","https://openalex.org/W4404180782","https://openalex.org/W6635898205","https://openalex.org/W6644808546","https://openalex.org/W6649450237","https://openalex.org/W6673456989","https://openalex.org/W6761132760","https://openalex.org/W6840505515","https://openalex.org/W6911232450","https://openalex.org/W6964454930"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"note":[2],"covers":[3],"some":[4,13,25,35,41],"of":[5,8,14,42],"the":[6,15,30,46],"history":[7],"Leonardo":[9],"numbers.":[10],"We":[11],"retrieve":[12],"most":[16],"recent":[17],"results":[18],"on":[19],"this":[20],"sequence,":[21],"as":[22,24],"well":[23],"relevant":[26],"historical":[27],"interconnections.":[28],"In":[29],"end,":[31],"we":[32],"also":[33],"provide":[34],"conjectures":[36],"and":[37],"open":[38],"problems":[39],"for":[40],"its":[43],"extensions":[44],"involving":[45],"modular":[47],"periodicity.":[48]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}