I don't think you're talking about triplets, I think you're talking about (Slayer-esque) bursts of three 16th notes followed by a 16th rest. A triplet would be three notes equally dividing the space it would take to fill two of those notes. In other words, an 8th note triplet would be three notes that take as much time as two 8ths. Most people count this as 'One-trip-let Two-trip-let Three-trip-let' etc.
You probably want to take a look at some thrash metal, I'd recommend Kreator and Slayer for your right hand. Or you could be a total badass and learn 'Bleed' (or anything else) by Meshuggah.