count-total-number-of-colored-cells.cpp

// Time:  O(1)
// Space: O(1)

// math
class Solution {
public:
    long long coloredCells(int n) {
        return 1LL * n * n + 1LL * (n - 1) * (n - 1);
    }
};

// Time:  O(1)
// Space: O(1)
// math
class Solution2 {
public:
    long long coloredCells(int n) {
        return (1 + (1 + 2LL * (n - 1))) * n / 2 * 2 - (2LL * n - 1);
    }
};