We are building a wall pergola that we want wisteria to grow on top of. The pergola will only come about 3.5-4 ft out from the wall (Edit: the columns themselves are less than 2ft from the wall). I have already placed 2 6x6 columns bolted into concrete on both sides. The beams are 16 ft apart.
Are there any wood (preferably cedar) beams that can span that 16' distance without having to place additional support in between? If so, what kind? Is there a chart somewhere with max distances that beams can span with minimal weight on top?
In the picture below, these beams span pretty far, but they are also very thick and I wonder if beams that thick can be mounted to a 6x6.

Edit:
If worried about the weight, see this wall pergola from Lowes. This would bear the weight with or without the long board in between the columns. This is what I am going to buy or build. I also have 6/6 columns on either side for wisteria to wrap around. I may or may not span a board from one column to the other, depending on if it makes sense to do so.