No of distinct strings possible under a condition

#include <iostream>
#include <vector>
using namespace std;

int main() {
   
   string s;
   cin>>s;
   int n = s.length();
   vector<vector<int>> dp(n , vector<int>(n));
   
   for(int g=0; g<n; g++){
       int i =0;
       int j=i+g;
       while( i < n && j < n){
           
           if(g == 0){
               dp[i][j] = 1;
           }else if(g == 1){
               if(s[i] == s[j]){
                   dp[i][j] = 2;
               }
               else{
                   dp[i][j] = 3;
               }
           }else{
               dp[i][j] = dp[i][j-1] + dp[i+1][j] - dp[i+1][j-1] + 1;
           }
           
          i++;
          j = i+g;
       }
   }
   
   cout<<dp[0][n-1];
   
}