I have this recurrence $p(n) = 2p(n-2) + n$, and I have guessed that the solution is $O(n^2)$, however, when I do the following calculations, I cannot get the inequality to hold
$p(n-2) \leq c(n-2)^2$ (induction hypothesis)
$2c(n-2)^2 + n \leq cn^2$ (substitution)
$cn^2-8c + n \leq cn^2$
Can anyone see where I go wrong? I also tried for even larger $O(n^x)$ but it still doesn't work.