Proof without Words: Odds and Squares

In the Mathematical Palette, my mathematics appreciation blog, I wrote about mathematics being a science of patterns. The images below only affirm the beauty of these patterns. they also show the intuitive proof of the statement, or what some people call proof without words.

Do you think the number pattern will continue as the number of circles increase? What conjectures can you make from the pattern?

Exercise: Prove your conjecture.