The recurrence $f_{n+1} = (t-2)f_n - f_{n-1}$ with $f_0=1$ and $f_1=t-1$ suggests that $f_n$ can be expressed in terms of Chebyshev polynomials as: $$f_n(t) = T_n(\tfrac{t-2}2) + \frac{t}{2} U_{n-1}(\tfrac{t-2}2)$$
Max Alekseyev
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