This solution is almost same as the DP solution for longest palindromic substring, instead of storing the longest, just get the count of palindromic substrings.

```
public int countSubstrings(String s) {
int n = s.length();
int res = 0;
boolean[][] dp = new boolean[n][n];
for (int i = n - 1; i >= 0; i--) {
for (int j = i; j < n; j++) {
dp[i][j] = s.charAt(i) == s.charAt(j) && (j - i < 3 || dp[i + 1][j - 1]);
if(dp[i][j]) ++res;
}
}
return res;
}
```