2579. Count Total Number of Colored Cells

There exists an infinitely large two-dimensional grid of uncolored unit cells. You are given a positive integer n, indicating that you must do the following routine for n minutes:

• At the first minute, color any arbitrary unit cell blue.
• Every minute thereafter, color blue every uncolored cell that touches a blue cell.

Below is a pictorial representation of the state of the grid after minutes 1, 2, and 3.

class Solution {
public:
    long long coloredCells(int n) {
        if(n == 1) return 1;
        return 2ll * n - 1 + 1ll * (n - 1) * (1ll + 2ll * n - 3ll);
    }
};