A Note on Bi-Periodic Leonardo Sequence - Catarino, Paula Maria Machado Cruz; Spreafico, Elen (Armenian Journal of Mathematics, 2024)
In this work, we define a new generalization of the Leonardo sequence by the recurrence relation GLe_n=aGLe_n-1+GLe_n-2+a (for even n) and GLe_n=bGLe_n-1+GLe_n-2+b (for odd n) with the initial conditions GLe_0=2a-1 and GLe_1=2ab-1, where a and b are real nonzero numbers. Some algebraic properties of the sequence {GLe_n}_n ≥ 0 are studied and several identities, including the generating function and Binet’s formula, are established.