Orthogonal polynomials related to a Jacobi symmetric matrix

Question

I would like to know if the following Hermitian tridiagonal (Jacobi) and symmetric matrix $A(t)$ \begin{equation} A(t)=\begin{bmatrix} 0&t&0&0&0&0&0&0&0\\ t&0&1&0&0&0&0&0&0\\ 0&1&0&t&0&0&0&0&0\\ 0&0&t&0&1&0&0&0&0\\ 0&0&0&1&0&1&0&0&0\\ 0&0&0&0&1&0&t&0&0\\ 0&0&0&0&0&t&0&1&0\\ 0&0&0&0&0&0&1&0&t\\ 0&0&0&0&0&0&0&t&0 \end{bmatrix}, \end{equation} with $t\geq 1$ and $t \in \mathbb{R}$, has a known family of orthogonal polynomials for any odd dimension $(2N+1)\times(2N+1)$. For t=1, they are Chebyshev polynomials of the second kind. If the answer is no, ¿could it be built from Chebyshev polynomials?