I think I've heard this rhythm before, what is it called? Where does it come from?
As Laurence shows, it's prevalent in pop culture as a crowd-participation chant. I'm used to it with the last two notes spoken as "Let's Go." It looks like it originated with a 1962 song by The Routers:
It looks like the opening clap/call material spread to cheerleading rather than the other way around. You can see more about its creation in the book Superstar in a Masquerade by William Sargent