# 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 $$a_n$$.

×