AMC 10B 2018 Problem 20

A function f is defined recursively by f(1)=f(2)=1 and

f(n)=f(n-1)-f(n-2)+n

for all integers n \geq 3. What is f(2018) ?

Answer Choices
A. 2016
B. 2017
C. 2018
D. 2019
E. 2020