A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence

In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation (for even n ) and (for odd n ) with the initial conditions . We obtained the characteristic function, generating function, and Binet’s formula for this sequence and propose a determinantal representation for the generating function of this sequence. We also provide some properties of these numbers. Moreover, we give the matrix representation of the biperiodic Leonardo numbers.