This is called as explanation brother 
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Try to run your program for n=5. Your program is giving incorrect answer i.e., 34. Correct answer is 35.
type or paste code here#include <iostream>
using namespace std;
int main() {
//o(1)
int t;
cin>>t;
while(t--)
{
int n;
cin>>n;
int ans=0;
if(n%2!=0){
int i=(n+1)/2;
ans=((2*i+1)*(i)*(2*i-1))/3;
}
else{
int i=n/2;
ans=(2*((2*i+1)*(i)*(i+1)))/3;
}
cout<<ans<<endl;
}
}
A nice and simple solution which is O(1) as well is n^2 + n choose 3 which can be simplified to the following expression:
#include <bits/stdc++.h>
using namespace std;
int main() {
int t;
cin >> t;
while(t–) {
int n;
cin >> n;
cout << (n**n) + ((n*(n-1)*(n-2))/6) << ‘\n’;
}
return 0;
}
Note I put two * since the website removes the multiplication but it just means n^2.