Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 7 / c / ii

The characteristic polynomial is $r^2-3r+2=(r-1)(r-2)$. Therefore $u_n=A+B{2}^n$. The initial values give $A+B=1$ and $A+2B=0$, yielding $A=2$, $B=-1$. HenceThe two constants are fixed by the two initial conditions of this second-order linear recurrence.