OIM 2017 Problem 3

Consider the configurations of integers $a_{1,1}$ $a_{2,1} a_{2,2}$ $a_{3,1} a_{3,2} a_{3,3}$ $\dots \dots \dots$ $a_{2017,1} a_{2017,2} a_{2017,3} \dots a_{2017,2017}$ Where $a_{i,j} = a_{i+1,j} + a_{i+1,j+1}$ for all $i,j$ such that $1 \leq j \leq i \leq 2016$ . Determine the maximum amount of odd integers that such configuration can contain.