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

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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