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Identities Involving the Fourth-Order Linear Recurrence Sequence
Open AccessArticle

Some New Identities of Second Order Linear Recurrence Sequences

by Yanyan Liu 1 and Xingxing Lv 2,*
1
School of Education, Xizang Minzu University, Xianyang 712082, China
2
School of Mathematics, Northwest University, Xi’an 710127, China
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1496; https://doi.org/10.3390/sym11121496
Received: 21 November 2019 / Revised: 4 December 2019 / Accepted: 5 December 2019 / Published: 10 December 2019
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. View Full-Text
Keywords: the second-order linear recurrence sequence; convolution sums; new identity; recurrence formula the second-order linear recurrence sequence; convolution sums; new identity; recurrence formula
MDPI and ACS Style

Liu, Y.; Lv, X. Some New Identities of Second Order Linear Recurrence Sequences. Symmetry 2019, 11, 1496.

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