Mersenne Lucas numbers and complete homogeneous symmetric functions Article Swipe

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Mersenne prime Homogeneous Lucas sequence Mathematics Lucas number Combinatorics Fibonacci number Fibonacci polynomials Orthogonal polynomials Difference polynomials

Nabiha Saba , Ali Boussayoud , Kasi Viswanadh V. Kanuri ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.22436/jmcs.024.02.04 · OA: W3121413093

In this paper, we first introduce new definition of Mersenne Lucas numbers sequence as, for n 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 (p, q)-numbers with Mersenne Lucas numbers at positive and negative indice.