Make your own Number Patterns

You can make your own number patterns using coins or matchsticks. Here is an example using coins:

sample pattern 1 sample pattern 2 sample pattern 3 sample pattern 4
Size=1 Size=2 Size=3 Size=4
1 Coin 6 Coins 15 Coins 28 Coins

How many coins do you need for Size=5 ?

Can you make a formula that will tell you how many coins are needed for any Size? For example Size=20? The formula may look something like

Coins = Size × Size + ...


(Note: There are lots of number patterns in Pascal's Triangle)