In this work, we define a new generalization of the Leonardo sequence by the recurrence relation GLeₙ=aGLeₙ₋₁+GLeₙ₋₂+a (for even n) and GLeₙ=bGLeₙ₋₁+GLeₙ₋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 ₙ ≥ 0 are studied and several identities, including the generating function and Binet's formula, are established.
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Catarino et al. (2024) studied this question.
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