{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:52:14Z","timestamp":1760241134769,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,12,10]],"date-time":"2019-12-10T00:00:00Z","timestamp":1575936000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Xizang N. S. F.","award":["XZ2017ZRG-65"],"award-info":[{"award-number":["XZ2017ZRG-65"]}]},{"name":"the N. S. F.","award":["11771351","11826205"],"award-info":[{"award-number":["11771351","11826205"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The main purpose of this paper is using the combinatorial method, the properties of the power series and characteristic roots to study the computational problem of the symmetric sums of a certain second-order linear recurrence sequences, and obtain some new and interesting identities. These results not only improve on some of the existing results, but are also simpler and more beautiful. Of course, these identities profoundly reveal the regularity of the second-order linear recursive sequence, which can greatly facilitate the calculation of the symmetric sums of the sequences in practice.<\/jats:p>","DOI":"10.3390\/sym11121496","type":"journal-article","created":{"date-parts":[[2019,12,10]],"date-time":"2019-12-10T10:52:41Z","timestamp":1575975161000},"page":"1496","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Some New Identities of Second Order Linear Recurrence Sequences"],"prefix":"10.3390","volume":"11","author":[{"given":"Yanyan","family":"Liu","sequence":"first","affiliation":[{"name":"School of Education, Xizang Minzu University, Xianyang 712082, China"}]},{"given":"Xingxing","family":"Lv","sequence":"additional","affiliation":[{"name":"School of Mathematics, Northwest University, Xi\u2019an 710127, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,10]]},"reference":[{"key":"ref_1","first-page":"149","article-title":"Some identities involving the Fibonacci numbers and Lucas numbers","volume":"42","author":"Zhang","year":"2004","journal-title":"Fibonacci Q."},{"key":"ref_2","first-page":"314","article-title":"Some identities involving the Fibonacci polynomials","volume":"40","author":"Yi","year":"2002","journal-title":"Fibonacci Q."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ma, Y.K., and Zhang, W.P. 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