if you plan to run a 4000 watt inverter and use it for long or very often you will need several panels to recharge if you are going to use often and several batteries to run long. on my M109a3 i plan to have 4 optima deep cycle batteries, 12 volt altenator, and several panels mounted on the roof to run a 1,500 to 2,500 watt inverter. there is a formula on battery usage in here somewhere one of the SS members posted.
the first picture is my barn and i have 2 heavy duty deep cycle batteries on it and i run lights and charge batteries in my rechargable tools and flash lights about twice a month with the sunforce solar panels. i use the harbor freight panles to charge my "Xantrex XPower Portable Powerpack 1500" which is a complete battery, 1,500 watt inverter, on wheels.
the second is my well house and i use the sunforce solar panels to charge one heavy duty deep cycle battery to run a 1,500 watt inverter to power my well at the back of my place. i have run it for as much as 2 hours but only do so about once a month during the summer.