I also attempted in c#, though mine might be more verbose.

static long substrCount(int n, string s) {

    int specialSubstringCount = 0;

    for (int i = 0; i < n  ; i++ ){
        for (int j = i + 1; j < n; j++){
             if(isSpecialSubstring(s.Substring(i, j - i + 1))){
                 specialSubstringCount += 1;
                 Console.WriteLine(specialSubstringCount);
             }
        }            
    }

    return n + specialSubstringCount;
}

//check if its a special substring
static bool isSpecialSubstring(string substring){

    //all characters are same
    bool allCharactersAreSame = true;
    StringBuilder builder = new StringBuilder(substring);
    Char currentCharacter = builder[0];     
    List<int> notSameIndexes = new List<int>();
    for (int i = 1 ; i < builder.Length; i++){
        if(builder[i] != currentCharacter){ 
               allCharactersAreSame = false;
               notSameIndexes.Add(i);         
        }
    }

     int midPoint = builder.Length / 2; 
    bool allCharactersExceptMiddleOneAreSame = notSameIndexes.Count() == 1 && notSameIndexes.First() == midPoint && builder.Length % 2 != 0;


    return allCharactersAreSame || allCharactersExceptMiddleOneAreSame;

    //all charaters except middle one are same

}