2018 Fermat Problem 21

A sequence has terms a_1, a_2, a_3, \ldots. The first term is a_1 = x and the third term is a_3 = y. The terms of the sequence have the property that every term after the first term is equal to 1 less than the sum of the terms immediately before and after it. That is, when n \geq 1, a_{n+1} = a_n + a_{n+2} - 1. The sum of the first 2018 terms in the sequence is

\textbf{(A)}\ -x - 2y + 2023\quad \textbf{(B)}\ 3x - 2y + 2017\quad \textbf{(C)} y \textbf{(D)}\ x + y - 1\quad \textbf{(E)}\ 2x + y + 2015

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