Given a generalized continued fraction g, for all n ≥ 1, we prove that the continuants function indeed satisfies the following recurrences:
Aₙ = bₙ * Aₙ₋₁ + aₙ * Aₙ₋₂, and Bₙ = bₙ * Bₙ₋₁ + aₙ * Bₙ₋₂.