There exist constants $r,$ $s,$ and $t$ so that
\[p(n) = rp(n - 1) + sp(n - 2) + tp(n - 3)\]for any quadratic polynomial $p(x),$ and any integer $n.$  Enter the ordered triple $(r,s,t).$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
There exist constants $r,$ $s,$ and $t$ so that
\[p(n) = rp(n - 1) + sp(n - 2) + tp(n - 3)\]for any quadratic polynomial $p(x),$ and any integer $n.$  Enter the ordered triple $(r,s,t).$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(3,-3,1)
There exist constants $r,$ $s,$ and $t$ so that
\[p(n) = rp(n - 1) + sp(n - 2) + tp(n - 3)\]for any quadratic polynomial $p(x),$ and any integer $n.$  Enter the ordered triple $(r,s,t).$
train