count-a-spiral

Count a Spiral

Your task is to return the amount of white rectangles in a NxN spiral. Your font may differ, if we talk of white rectangles, we talk about the symbols in the top row.

Notes:

• As a general rule, the white snake cannot touch itself.
• The size will be at least 5.
• The test cases get very large, it is not feasible to calculate the solution with a loop.

Examples

For example, a spiral with size 5 should look like this:

⬜⬜⬜⬜⬜
⬛⬛⬛⬛⬜
⬜⬜⬜⬛⬜
⬜⬛⬛⬛⬜
⬜⬜⬜⬜⬜

And return the value 17 because the total amount of white rectangles is 17.

---

A spiral with the size 7 would look like this:

⬜⬜⬜⬜⬜⬜⬜
⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬜⬜⬜⬛⬜
⬜⬛⬛⬛⬜⬛⬜
⬜⬛⬜⬜⬜⬛⬜
⬜⬛⬛⬛⬛⬛⬜
⬜⬜⬜⬜⬜⬜⬜

And return the value 31 because the total amount of white rectangles is 31.

---

A spiral with the size 8 would look like this:

⬜⬜⬜⬜⬜⬜⬜⬜
⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬜⬜⬜⬜⬛⬜
⬜⬛⬛⬛⬛⬜⬛⬜
⬜⬛⬜⬛⬛⬜⬛⬜
⬜⬛⬜⬜⬜⬜⬛⬜
⬜⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬜⬜⬜⬜⬜⬜

And return the value 39 because the total amount of white rectangles is 39.

---

A spiral with the size 9 would look like this:

⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬜
⬜⬛⬛⬛⬛⬛⬜⬛⬜
⬜⬛⬜⬜⬜⬛⬜⬛⬜
⬜⬛⬜⬛⬛⬛⬜⬛⬜
⬜⬛⬜⬜⬜⬜⬜⬛⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜

And return the value 49 because the total amount of white rectangles is 49.

---

A spiral with the size 10 would look like this:

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜
⬜⬛⬛⬛⬛⬛⬛⬜⬛⬜
⬜⬛⬜⬜⬜⬜⬛⬜⬛⬜
⬜⬛⬜⬛⬛⬜⬛⬜⬛⬜
⬜⬛⬜⬛⬛⬛⬛⬜⬛⬜
⬜⬛⬜⬜⬜⬜⬜⬜⬛⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

And return the value 59 because the total amount of white rectangles is 59.