Question 138
Given a positive integer $n$, a triangular array $(a_{i,j})$ of zeroes and ones, where $i$ and $j$ run through the positive integers such that $i + j \le n + 1$, is called a *binary anti-Pascal n-triangle* if $a_{i,j} + a_{i,j+1} + a_{i+1,j} \equiv 1 \pmod 2$ for all possible values $i$ and $j$ may take on. Determine the minimum number of ones a binary anti-Pascal $n$-triangle may contain.