Have you simply washed the sheets or did you also use an enzymatic cleaner as well? He'll continue peeing where he smells his pee. You need somethign like Nature's Miracle to remove all the particles of pee so that he no longers smells he's been there. Do you have a rubber sheet under your sheet? There's something about rubber that makes cats pee. Allen can't resist the rubber backed bathmats.

My first inclination is exactly what Catty said: is he neutered and has he been checked for a urinary problem? Belive me, for years I swore Allen was a behavioral peer.... and he only pees when he has an infection (like he does right now) I thought I knew my cat, but cats hide infection and illness very well.