Poor Arthur. Constipation is rubbish.
I'm much more mindful of what Alice eats now after I inadvertently inflicted constipation on her a few weeks back. I was effectively giving her too much of the BRAT diet (Banana, Rice, Apple and Toast). Good for helping with D+V in a poorly baby, not so good for a healthy baby to poop! There was also too much steamed carrots, potato, swede, cheese and yoghurt in her diet, which didn't help.
Now, I make sure she gets Weetabix with a handful of berries a few times a week. She still gets BRAT stuff, but not as much of it. I've also swapped to half and half bread for sandwiches and toast. I second getting lots of water each meal. I give the sippy cup to Alice and let her go to town. All this seems to be working well for us as Alice is going once a day again.
Try other 'P' fruits? Pears, plums and peaches, as well as prunes, are good for constipation. Adding a little pear/prune juice to his water in top of the purees could help. Berries are good too. Swapping to sweet potato instead of regular potato might be a good idea too. My friend's baby had to have bananas completely cut out of his diet for a few months as they'd stuff him completely.
Keep doing what you're doing, and he'll soon be right as rain. With nappies both bountiful and regular!