Hello everyone, I am trying to solve Move and Turn problem on codeforces. Basically, the problem says that "A Robot is standing at origin and can choose any of the 4 directions to move in 1st step, then it should turn $$$90^\circ$$$ either to left or right at every step. Now, given that Robot has made exactly $$$n$$$ steps, then what is the number of unique points robot can be present at?"

I got the solution presented in the editorial but there is a DP solution given in the comments, which I am trying to understand but not able to.

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll a[1005];
int main()
{
    int n;
    cin>>n;
    a[0]=1;a[1]=4;a[2]=4;
    for(int i=3;i<=n;i++)
        if(i&1) a[i]=4*((i+1)/2)+a[i-2];
        else a[i]=4*((i+1)/2)+a[i-4];
        cout<<a[n];
}

If someone can help me in understanding it, I would highly appreciate it.