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In this paper, we first introduce new definition of Mersenne Lucas numbers sequence as, for \ (n 2, \) \ (m₍=3m₍-₁-2m₍-₂\) with the initial conditions \ (m₀=2\) and \ (m₁=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.
Saba et al. (Thu,) studied this question.