Solution
= Solution
Let $\phi=(1+\sqrt5)/2$, the <golden ratio>. Since $\phi^2=\phi+1$, multiplication by $\phi^n$ gives $\phi^{n+2}=\phi^{n+1}+\phi^n$. Adding this <recurrence relation> to the one for $A_n$ yields
$$
\boxed{B_{n+2}=B_{n+1}+B_n,\qquad B_0=3,\quad B_1=2+\phi.}
$$
Thus the extra exponential term changes the initial values, but not the <linear recurrence relation>.