Computing Image Circle at different magnifications?

[resummerfield]

I’m trying to compute the Image Circle of a lens at different distances. If the lens covers 300mm at infinity, it should cover 600mm at 1:1. But what about 1:3, where the film image is 1/3 the size of the actual subject? Before I purchase a lens for my enlarger, I'd like to compute if it will in fact cover the negative at a 3x enlargement. I’m brain-dead today, and can’t remember the formula.