Let us call a sum of integers a cool sum if the first and last terms are $$1$$ and each term differs from its neighbours by at most. For example, $$1+2+2+3+3+2+1$$ and $$1+2+3+4+4+3+2+1$$ are cool sums. The minimum number of terms required to write $$2019$$ as a cool sum is

To maximize the sum with a fixed number of terms, increase by $$1$$ from $$1$$ to a peak and then decrease by $$1$$ back to $$1$$, with a repeated peak when necessary. The construction reaching $$2019$$ uses $$89$$ terms, with the central values rising through $$44$$ and then descending symmetrically. Therefore the minimum number of terms is $$89$$.