Generating a sequence of squares

         A few years ago,, I set myself the

daunting challenge of writing the squares of
all the numbers till 105.

         I discovered an easy shortcut. It goes like this.
Take 2. The square is 4.
Take 3. The square is 9 (=4 + 2 + 3)
Take 4. The square is 16 (=9 + 3 + 4)

The formula, therefore, is as follows:

Take n. The square is obtained by (n-1)² + n + (n-1)

This formula works if you wish to generate all the squares
in sequence without using a calculator.

             PS: This formula is not as original as I thought initially.
This is very easy to visualize. I found this subsequently in
one of the books of the Murderous Maths series. It goes
as follows:

            Take 9 coins and form a 3x3 square. If I now want to
make a 4x4 square, what do I need? I need a column of 4 coins
and a row of 3 coins. There this is identical to what is said above.