3 and 1 broken twill
The 3/1 part of the name refers to the fact that the floats are built up by the top thread floating over the top of the band for three rows, then under for one.
The combination of these causes a double-faced weave that allows for nice, crisp 45-degree pattern lines. The draw-back being that lines orthogonal to the band (ie across the width of it) can never be crisp and straight.
For a full discussion of the technique, refer to Phiala's 3/1 twill tutorial: http://www.stringpage.com/old/twill.html