2017 OIM Problems/Problem 3

Problem

We consider configurations of integers:

$a_{1,1},\\ a_{2,1}, a_{2,2},\\ a_{3,1}, a_{3,2}, a_{3,3},\\ \cdots\\ a_{2017,1}, a_{2017,2}, a_{2017,3},\cdots,a_{2017,2017}$

with $a_{i,j} = a_{i+1,j} + a_{i+1,j+1}$ for all $i, j$ such that $1 \le j \le i \le 2016$ . Find the maximum number of odd integers that such a configuration can contain.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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2017 OIM Problems/Problem 3

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