MathDB

A series of figures is shown in the picture below, each one of them created by following a secret rule. If the leftmost figure is considered the first figure, how many squares will the 21st figure have?
http://www.artofproblemsolving.com/Forum/download/file.php?id=49934
Note: only the little squares are to be counted (i.e., the

2 \times 2

squares,

3 \times 3

squares,

\dots

should not be counted)
Extra (not part of the original problem): How many squares will the 21st figure have, if we consider all

1 \times 1

squares, all

2 \times 2

squares, all

3 \times 3

squares, and so on?.

Problem Statement