Mersenne Lucas numbers and complete homogeneous symmetric functions

Volume 24, Issue 2, pp 127--139 http://dx.doi.org/10.22436/jmcs.024.02.04

Publication Date: January 21, 2021 Submission Date: September 20, 2020 Revision Date: December 13, 2020 Accteptance Date: December 27, 2020

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Authors

Nabiha Saba - LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria. Ali Boussayoud - LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria. Kasi Viswanadh V. Kanuri - 3669 Leatherwood Dr, Frisco, TX 75033, USA.

Abstract

In this paper, we first introduce new definition of Mersenne Lucas numbers sequence as, for \(n\geq 2,\) \(m_{n}=3m_{n-1}-2m_{n-2}\) with the initial conditions \(m_{0}=2\) and \(m_{1}=3\). Considering this sequence, we give Binet's formula, generating function and symmetric function of Mersenne Lucas numbers. By using the Binet's formula we obtain some well-known identities such as Catalan's identity, Cassini's identity and d'Ocagne's identity. After that, we give some new generating functions for products of \(% \left( p,q\right) \)-numbers with Mersenne Lucas numbers at positive and negative indice.

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Keywords

• Mersenne Lucas numbers
• \(\left(p,q\right) \)-numbers
• symmetric functions
• Binet's formula
• generating functions

MSC

•  05E05
•  11B39

References

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