Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$ What I get is $4 \cdot 54k + 27(n(n-1)) - 2$.
I understand first two terms but $-2$ is giving me a headache. I suppose to be true every term should be divisible by $54$. Or did I make wrong conclusion?
P. S: Is there mathjax tutorial?

$2^{2n+1}-9n^2 +3n -2 = 54k$ 
$2^{2n+1} =54k +9n^2 -3n +2$
$2^{2(n+1)+1} -9(n+1)^2 +3(n+1) -2=$ 
$2^2(54k +9n^2 -3n +2) -9(n+1)^2 +3(n+1) -2$
After I compute everything, I get this: $4\cdot54k +27(n(n+1)) -2.$
