MathNet 2022-part-02 — 197 problems (EN–VI) Question 30

Find the least possible sum of 2021 terms of the sequence of integers $a_1, a_2, a_3, \dots$, where $a_1 = 0$, $a_2 = a_3 = 1$ and $a_{i+j} \gt a_i + a_j$ for every $i, j \ge 2$.