Lighting, Light Fixtures, Ceiling and Exhaust Fans - replacing fan with recessed lights

I have looked all over for a diagram that matches this scenario, but I can't find one.

I am replacing the ceiling fan in my kitchen with two recessed lights. The fan is controlled by one switch, and as far as I can tell, there are no other receptacles in this circuit.

The switch has two black wires attached, and one red wire attached, and two white wires taped together. The hole in the ceiling has two sets of wires, seeming to come from different directions. One set has a black, white, and bare ground. The other set has a black, a white, and a red.

I attached a can light to each set to try to figure out what was going on, and when I attached a light to the set with the ground wire, the light came on. When I attached a light to the set with the red wire, the light did not come on.

What should I do?:confused:

When you took the fan down, did you happen to notice if the two black wires in the ceiling box were connected together?

If so you need to connect them back together. You should then find that the red wire in the other cable is hot when you turn on the switch but not hot when the switch is turned off.

I didn't notice, because the fan was heavy and I was trying to disconnect the wires as fast as possible. But I'll try that and experiment! Thanks!