{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:14:15Z","timestamp":1746803655450,"version":"3.40.5"},"reference-count":11,"publisher":"Wiley","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>We introduce three new two-parameter generalizations of Fibonacci numbers. These generalizations are closely related to<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:math>-distance Fibonacci numbers introduced recently. We give combinatorial and graph interpretations of distance<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>r<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>k<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-Fibonacci numbers. We also study some properties of these numbers.<\/jats:p>","DOI":"10.1155\/2015\/879510","type":"journal-article","created":{"date-parts":[[2015,9,14]],"date-time":"2015-09-14T17:02:28Z","timestamp":1442250148000},"page":"1-6","source":"Crossref","is-referenced-by-count":0,"title":["On Distance<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>r<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>k<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-Fibonacci Numbers and Their Combinatorial and Graph Interpretations"],"prefix":"10.1155","volume":"2015","author":[{"given":"Dorota","family":"Br\u00f3d","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Applied Physics, Rzesz\u00f3w University of Technology, Aleja Powsta\u0144c\u00f3w Warszawy 12, 35-959 Rzesz\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"year":"2005","key":"2"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.09.022"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2006.10.071"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.10.022"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2008.11.031"},{"key":"9","first-page":"139","volume":"55","year":"2000","journal-title":"Ars Combinatoria"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2007.03.004"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2007.10.007"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/491591"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2013.05.029"},{"key":"1","first-page":"391","volume":"118","year":"2015","journal-title":"Ars Combinatoria"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/879510.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/879510.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/879510.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,18]],"date-time":"2016-08-18T23:10:29Z","timestamp":1471561829000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2015\/879510\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":11,"alternative-id":["879510","879510"],"URL":"https:\/\/doi.org\/10.1155\/2015\/879510","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2015]]}}}