Recurring Styles 10 - Simultaneous System of Recurrences!

\[\large{\begin{cases} D_{n+1} = 8L_n + 39n - 9 \\ D_n + 9n = L_n + 6n = K_{3n} + 33n \\ L_0 = D_0 = K_0 = 1 \end{cases}}\]

Solve the system of recurrences with respect to \(K_n, L_n\) and \(D_n\) in terms of \(n\) for \(n \geq 0\). Submit the value of \((D_6 - K_{15} - L_5)\) as your answer.

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