The First Study of Mersenne--Leonardo Sequence

In this study, we introduce a new class of numbers, referred to as Modified Mersenne--Leonardo numbers. The aim of this paper is to define the Modified Mersenne--Leonardo sequence and investigate some of its properties, including the recurrence relation, summation formula, and generating function. Additionally, classical identities such as the Tagiuri–Vajda, Catalan, Cassini, and d’Ocagne identities are derived for the Modified Mersenne--Leonardo numbers.