On Mersenne- Narayana and Mersenne- Narayana - Lucas Sequences

Resumen

The objective is to generate Mersenne-Narayana and Mersenne-Narayana-Lucas Sequences. Third-order recurrence relations corresponding to Mersenne-Narayana and Mersenne-Narayana-Lucas Sequences are introduced. For the aforementioned sequences, recurrence relations, generating functions, and Binet formulas are then found. These sequences have been verified through some well-known identities. Some identities have been provided using the matrix approach. This paper presents the introduction of two novel sequences, specifically the Mersenne-Narayana and Mersenne-Narayana-Lucas Sequences, accompanied by their respective recurrence relations, Binet formulas and some connected identities.