Recurring Styles #1 - Direct Parametric Recurrence!

Algebra Level 5

an+1=2ann2+n \large{a_{n+1} = 2a_n - n^2 + n}

Define a sequence ana_n that satisfy the recurrence relation as described above, with a1=3a_1 = 3 . Find the value of a20a1518133 \dfrac{ |a_{20} - a_{15} | }{18133} .

Bonus: Generalize this for all values of ana_n .

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