2579. Count Total Number of Colored Cells ¶

Problem

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.

Return the number of colored cells at the end of n minutes.

Example 1:

Input: n = 1
Output: 1
Explanation: After 1 minute, there is only 1 blue cell, so we return 1.

Example 2:

Input: n = 2
Output: 5
Explanation: After 2 minutes, there are 4 colored cells on the boundary and 1 in the center, so we return 5.

Constraints:

1 <= n <= 10⁵