A recurrence in matrix form is (anan−1)=(2110)(an−1an−2)\begin{pmatrix} a_n \\ a_{n-1} \end{pmatrix} = \begin{pmatrix} 2 & 1 \\ 1 & 0 \end{pmatrix} \begin{pmatrix} a_{n-1} \\ a_{n-2} \end{pmatrix}(anan−1)=(2110)(an−1an−2). What is the recurrence relation?
an=2an−1+an−2a_n = 2a_{n-1} + a_{n-2}an=2an−1+an−2
an=an−1+2an−2a_n = a_{n-1} + 2a_{n-2}an=an−1+2an−2
an=2an−1−an−2a_n = 2a_{n-1} - a_{n-2}an=2an−1−an−2
an=an−1+an−2a_n = a_{n-1} + a_{n-2}an=an−1+an−2