Some New Identities of Second Order Linear Recurrence Sequences
by
Yanyan Liu 1 and Xingxing Lv 2,*
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
(This article belongs to the Special Issue The 32th Congress of The Jangjeon Mathematical Society (ICJMS2019) will be Held at Far Eastern Federal Universit, Vladivostok Russia)
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.
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Keywords:
the second-order linear recurrence sequence; convolution sums; new identity; recurrence formula
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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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