sonant?

$(2)$ Find the solution to the recurrence relation $a_n=3a_{n-1}-2a_{n-2}+2^n$

with initial conditions $a_0=1$ and $a_1=4.$

$(3)$ Create a Huffmann code for the following frequencies

$A=\mathrm{.}20,M=\mathrm{.}09,U=\mathrm{.}06,S=\mathrm{.}17,E=\mathrm{.}35,R=\mathrm{.}13$