After getting destroyed by the problem mentioned in this blog

I decided to get revenge on the problemsetter(dvdg6566) by setting a problem related to his that he couldn't solve :). After thinking a while I came up with this problem. Given two integers N and I, construct a sequence of non-negative integers with length N with inequality I where inequality is defined as

$$$I = \sum\limits_{i=1}^N \bigg( \sum\limits_{j=i}^N rangemax(i,j) \bigg)$$$

But after thinking a while again, I realized I couldn't solve it either. I could only construct a solution for $$$I>=(2*(n-1)*(n-2))$$$ but for smaller I, I have no idea how to do it. Any help would be appreciated thanks!.