Let W is WHITE, R is RED, B is BLUE
So for n=1:
f(n)=2
W or R;
for n=2:
f(n)=2 too
WR or RW;
And now the most interesting:
for n=3:
f(n)=
We add to combinations of n-1 W or R:  WRW or RWR;
+
We add to combinations of n-2 RB or WB: RBW or WBR;
=f(n-1)+f(n-2);
So you can check it for n=4 and n=5///It's really easy