Observation:
The preceding method is too cool because it gives the impression of a number of palindrome substrings of length 5, whereas the preceding method is o(n^2) using 2 DP. Cant we reduced to o(n) by using 3 dp. Yes we can becuase here n should should be length of string but next 2 parameters length lie in range 0 to 25.
Eg: dp[i][j][k] j, k is between 0 and 25. i is between 0 and the length of the string.
We can't get an idea directly from observation, so go to the institution.
