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In this work, we define a new generalization of the Leonardo sequence by the recurrence relation GLeₙ=aGLe₍-₁+GLe₍-₂+a (for even n) and GLeₙ=bGLe₍-₁+GLe₍-₂+b (for odd n) with the initial conditions GLe₀=2a-1 and GLe₁=2ab-1, where a and b are real nonzero numbers. Some algebraic properties of the sequence \GLeₙ\₍ ₀ are studied and several identities, including the generating function and Binet's formula, are established.
Catarino et al. (Tue,) studied this question.