Recurring Styles #1 - Direct Parametric Recurrence!

Algebra Level 5

\[ \large{a_{n+1} = 2a_n - n^2 + n} \]

Define a sequence \(a_n\) that satisfy the recurrence relation as described above, with \(a_1 = 3 \). Find the value of \( \dfrac{ |a_{20} - a_{15} | }{18133} \).

Bonus: Generalize this for all values of \(a_n \).

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