Calculus of order of algorithm

Question

I want to calculate the order of this function, I calculated but I'm not sure if this right.

This is the function

int fct (int Y){
        int y = 0 ;
        for ( int i =0; i<Y;++ i ){
            for ( int j=i ; j >=0;--j ){
                y++;
                }
            }
            return y ;
    }

And this is my calculus:

For Inner Loop

\1+1+sum_{j=i}^{n-1}(1+1+1)=3n-1

For First loop

\1+1+sum_{i=o}^{n}(3n-1+1)=3n^{2}+2

Finally 3n^{2}+1+2=3n^{2}+3= O(n^{2})

Its right this solution?

Thanks