Formula for number of dominoes

So I was trying to wrap my head around the formula for the number of dominoes.

It's (n+1)(n+2)/2.

For double 12 dominoes, that's 91. But how to derive it?

Let's look at the simple case of n=2 dominoes.

Plugging n=2 into the formula, we get (3)(4)/2 or 6 dominoes.



but there's tiles that stick out over the top of the triangle. There's (n+1) half tiles. Or (n+1)/2 area, to sum up all the half tile area.



and presto we get our formula:

((n+1)(n+1)/2) + ((n+1)/2)

and simplifying

(n^2+2n+1)/2 + (n+1)/2

to get

(n^2 + 3n + 2)/2

or

(n+1)(n+2)/2.


http://www.domino-games.com/faq/How-Many-Tiles-And-Dots-Are-In-A-Dominoes-Set.html

Math and dominoes...