On some combinatorial properties of Leonardo-Mersenne sequence

New number sequence, namely, the Leonardo-Mersenne sequence is introduced in this paper. We investigate the Binet-like formula, partial sum, generating function and exponential generating function related to this sequence. Interesting identities and summation formulas of this sequence are stated in this paper. Then we apply the binomial transform to this sequence and study some identities and summation formulas of it. In order to highlight the results, some numerical examples are given in this paper.

Keywords:

Leonardo number , Mersenne sequence , Binet Formula , Summation formula , Binomial transform