Virbration at 32-42 mph

I have a 2006 Tundra Limited Double cab 4x4 with 12,300 miles on it. When driving at or near 32-42 mph the truck has a bad vibration. It's like you are driving on the rumble strips cut into the road prior to coming to a stop sign. It only happens at that speed. Anything higher or lower there's no vibration. I also tried turning off the overdrive, and it's not there when the overdrive is shut off. If you turn the overdrive back on it's there. If you"feather" the gas to get through that speed it won't virbrate. If you give it more gas and get through that area it doesn't do it. It's only when you drive normally, medium acceleration back off on the throttle at 30 mph slowly increasing to 35-40 and wow, there it is. If it starts to vibrate I can turn off the overdrive and it stops.
I've checked the tires and there ok (I can run up to 80 mph with no vibration)
The drive shaft has not lost any balance weights.
Could the lack of driving have something sticking?