# Lucky money new year

$\large (u_{n}): \begin{cases} u_{0}=-1 \\ u_{1}=3, \quad \forall n\geq 1 & \\ u_{n}-5u_{n-1}+6u_{n-2}=2n^{2}+2n+1 & \end{cases}$

Consider the recurrence relation above.

If $$u_{n}$$ can be expressed as $$u_{n}=ab^n +cd^n +en^k +fn^l +g$$, type your answer as $$a+b+c+d+e+f+g+k+l$$

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