{"id":"https://openalex.org/W2975503327","doi":"https://doi.org/10.3390/sym11101195","title":"Tribonacci Numbers and Some Related Interesting Identities","display_name":"Tribonacci Numbers and Some Related Interesting Identities","publication_year":2019,"publication_date":"2019-09-24","ids":{"openalex":"https://openalex.org/W2975503327","doi":"https://doi.org/10.3390/sym11101195","mag":"2975503327"},"language":"en","primary_location":{"id":"doi:10.3390/sym11101195","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11101195","pdf_url":"https://www.mdpi.com/2073-8994/11/10/1195/pdf?version=1569309022","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/10/1195/pdf?version=1569309022","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102127931","display_name":"Shujie Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I37802460","display_name":"Northwest University","ror":"https://ror.org/00z3td547","country_code":"CN","type":"education","lineage":["https://openalex.org/I37802460"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shujie Zhou","raw_affiliation_strings":["School of Mathematics, Northwest University, Xi\u2019an 710127, China","School of Mathematics, Northwest University, Xi'an 710127, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Northwest University, Xi\u2019an 710127, China","institution_ids":["https://openalex.org/I37802460"]},{"raw_affiliation_string":"School of Mathematics, Northwest University, Xi'an 710127, China","institution_ids":["https://openalex.org/I37802460"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100379179","display_name":"Li Chen","orcid":"https://orcid.org/0000-0001-8175-3650"},"institutions":[{"id":"https://openalex.org/I37802460","display_name":"Northwest University","ror":"https://ror.org/00z3td547","country_code":"CN","type":"education","lineage":["https://openalex.org/I37802460"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Li Chen","raw_affiliation_strings":["School of Mathematics, Northwest University, Xi\u2019an 710127, China","School of Mathematics, Northwest University, Xi'an 710127, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Northwest University, Xi\u2019an 710127, China","institution_ids":["https://openalex.org/I37802460"]},{"raw_affiliation_string":"School of Mathematics, Northwest University, Xi'an 710127, China","institution_ids":["https://openalex.org/I37802460"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100379179"],"corresponding_institution_ids":["https://openalex.org/I37802460"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.7356,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.70845481,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"11","issue":"10","first_page":"1195","last_page":"1195"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":1.0,"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":1.0,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T14500","display_name":"Advanced Mathematical Theories","score":0.9926999807357788,"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/series","display_name":"Series (stratigraphy)","score":0.6884303092956543},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6212687492370605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5726520419120789},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34821948409080505},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.307966023683548},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06510323286056519}],"concepts":[{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6884303092956543},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6212687492370605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5726520419120789},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34821948409080505},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.307966023683548},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06510323286056519},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym11101195","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11101195","pdf_url":"https://www.mdpi.com/2073-8994/11/10/1195/pdf?version=1569309022","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:20ff7804e719467cada5081e017926b5","is_oa":true,"landing_page_url":"https://doaj.org/article/20ff7804e719467cada5081e017926b5","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 10, p 1195 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11101195","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11101195","pdf_url":"https://www.mdpi.com/2073-8994/11/10/1195/pdf?version=1569309022","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4970092474","display_name":null,"funder_award_id":"11771351","funder_id":"https://openalex.org/F4320315254","funder_display_name":"Innovative Research Group Project of the National Natural Science Foundation of China"},{"id":"https://openalex.org/G6753436512","display_name":null,"funder_award_id":"11826205","funder_id":"https://openalex.org/F4320315254","funder_display_name":"Innovative Research Group Project of the National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320315254","display_name":"Innovative Research Group Project of the National Natural Science Foundation of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2975503327.pdf","grobid_xml":"https://content.openalex.org/works/W2975503327.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W121432882","https://openalex.org/W129481463","https://openalex.org/W1495550473","https://openalex.org/W1531176002","https://openalex.org/W1975841905","https://openalex.org/W1978706659","https://openalex.org/W2016115496","https://openalex.org/W2073328732","https://openalex.org/W2145713937","https://openalex.org/W2286411715","https://openalex.org/W2396250052","https://openalex.org/W2403019421","https://openalex.org/W2580194929","https://openalex.org/W2600405718","https://openalex.org/W2736223503","https://openalex.org/W2758784115","https://openalex.org/W2899745446","https://openalex.org/W2904526393","https://openalex.org/W2949176902","https://openalex.org/W2949984441","https://openalex.org/W2950432683","https://openalex.org/W2963098067","https://openalex.org/W4292806204","https://openalex.org/W6631671827","https://openalex.org/W6644115537","https://openalex.org/W6711900087","https://openalex.org/W6724796258","https://openalex.org/W6732358713","https://openalex.org/W6764081330"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"The":[0],"main":[1],"purpose":[2],"of":[3,14,23],"this":[4],"paper":[5],"is,":[6],"by":[7],"using":[8],"elementary":[9],"methods":[10],"and":[11,33],"symmetry":[12],"properties":[13],"the":[15,20,30],"summation":[16],"procedures,":[17],"to":[18,29,34],"study":[19],"computational":[21],"problem":[22],"a":[24],"certain":[25],"power":[26],"series":[27],"related":[28],"Tribonacci":[31],"numbers,":[32],"give":[35],"some":[36],"interesting":[37],"identities":[38],"for":[39],"these":[40],"numbers.":[41]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}