Planted them in 3s is a very old tradition, and has many possible, but unknown origins. One is that they just look better together, another is the roots are crowded and keeps them from getting too tall.The seeds are very light and germinate easily, so they are commonly the first trees to sprout after a forest fire in places where they are native. They can live 100 years but most in gardens do not, and most die at 20-30 years. One big problem is that they are a favorite for destructive woodpeckers. You can surely plant just one if you want to, and not worry about the "Birch Police" getting you.