Chapter 4 - Eigenvalues and Eigenvectors - 4.6 Applications and the Perron-Frobenius Theorem - Exercises 4.6 - Page 361: 48

See below.

If $x_n=2x_{n-1}+x_{n-2}$ and $x_0=1,x_1=1$, then: $x_2=2x_1+x_0=2\cdot1+1=3$ $x_3=2x_2+x_1=2\cdot3+1=7$ $x_4=2x_3+x_2=2\cdot7+3=17$ $x_5=2x_4+x_3=2\cdot17+7=41$ $x_6=2x_5+x_4=2\cdot41+17=99$ $x_7=2x_6+x_5=2\cdot99+41=239$