Tessellate S.T.E.M.S. (2019) - Mathematics - Category A (School) - Set 5 - Objective Problem 1

Let $0=a_0 < a_1 < a_2 < ...$ be integers such that for all $n \in \mathbb{N}$ , there exists a unique triple $(i,j,k)$ of non-negative integers satisfying $a_i + 2a_j + 4a_k = n$ . Compute the value of $a_{1998}$ .

This problem is a part of Tessellate S.T.E.M.S. (2019)