Malak, how'd you make that picture, is it an html table?
also, sorry to be an internet jerk, (honestly i really am a real person who doesn't like to be a jerk) BUT.....
this pattern doesn't actually increase efficiency. I don't understand your calculations, but I think you may have made a mistake somewhere. To calculate the efficiency of a repeating pattern (this is called a packing problem) you need to take the smallest repeatable unit of the pattern and divide the filled space by the total space. that will give you the ratio of empty space to filled space.
on the original rows pattern, your efficiency is 1 road for 2 solar panels, so thats 2 out of 3, or 66.66%. on your new pattern, your smallest repeatable cell is 3 solar panels for 2 blank spaces (1 road, one completely blank) which gives you an efficiency of 3 out of 5, also known as 60.00%.
You could say that the whole 5x4 block (in green) is the repeating cell, but that still gives you an efficiency of 12 out of 20 which is still 60.00% rows are 6% more efficient than the pattern in your first post.
One idea I had was to try a Hilbert curve. this is a 'curve' designed to cover a plane using a repeating pattern of straight lines. its not designed to be efficient, and turns out, it doesnt increase efficiency over rows either. I'm not saying there's not a more efficient way to do it, but we haven't found it in this thread so far.