Math Puzzle. How many pips are on a Double Nine set of dominoes?

A domino is a rectangular tile. The dots, called pips, represent the two numbers on the tile. The Double Six set of dominoes consists of every pairgin of numbers from 0 to 6 (i.e.,0-0,1-0,1-1, ...,6-6). Sets arfe also available in Double Nine, Double Twelve, Double Fifteen and Doulbe Eighteen. How many pips are on a Double Nine set of dominoes?Math Puzzle. How many pips are on a Double Nine set of dominoes?
Well.. here's what I'm thinking.



First, I started by trying to show what happens when you have smaller sets of dominoes. Let's look at what happens when you have only two possible numbers:

0-0, 0-1, 1-1

So 3 pips. Then, let's add another possible number:

0-2, 1-2, 2-2

Combined with the above, that gives us 12 pips.

0-3, 1-3, 2-3, 3-3

Combined with above, 30 pips

0-4, 1-4, 2-4, 3-4, 4-4

Combined with above, 60 pips

0-5, 1-5, 2-5, 3-5, 4-5, 5-5 = 105 pips



So the sequence is 3, 12, 30, 60, 105

Differences = 9, 18, 30, 45

Differences of differences = 9, 12, 15



So the next number would 105 + 45 + 18 = 168.



So there's our sequence. This can evaluate to:

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



So a Double Nine would have: 9 * 10 * 11 / 2 = 495 pips