1-1 Correspondence

Hi,

Could anyone help me understand (by way of a link or explanation) how
the formula (1/2)*[(a+b)^2 + 3a + b] provides an explicit 1-1
correspondence between the natural numbers and the pairs (a,b) of
natural numbers?

Have come across this as an exercise in a book but can't figure out a
way to see it.

Thanks for any help,
Mitch.
.