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: $$f_n(t) = T_n(\tfrac{t-2}2) + \frac{t}{2} U_{n-1}(\tfrac{t-2}2)$$

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: \begin{split} f_n(t) &= T_n(\tfrac{t}2-1) + \frac{t}{2} U_{n-1}(\tfrac{t}2-1) \\ &=U_n(\tfrac{t}2-1) + U_{n-1}(\tfrac{t}2-1), \end{split} and so their orthogonality and other properties should follow from those of Chebyshev polynomials.