Count of strings that can be formed using a, b and c under given constraints

Given a length n, count the number of strings of length n that can be made using ‘a’, ‘b’ and ‘c’ with at-most one ‘b’ and two ‘c’s allowed.

• Time : O(1)
• Space : O(1)

c++

long long int countStr(long long int n){
    if(n == 1) return 3;
    if(n == 2) return 8;
    long long int res = 0;
    for(long long int b = 0; b <= 1; b++) {
        for(long long int c = 0; c <= 2; c++) {
            if(b == 0 and c == 0) res += 1;
            if(b == 0 and c == 1) res += n;
            if(b == 0 and c == 2) res += n * (n - 1) / 2;
            if(b == 1 and c == 0) res += n;
            if(b == 1 and c == 1) res += n * (n - 1);
            if(b == 1 and c == 2) res += n * (n - 1) * (n - 2) / 2;
        }
    }
    return res;
}