Here's a sort of a blues rhumba groove by Al Jackson, Jr.. The song is Crosscut Saw, from Albert King's classic album, Born Under A Bad Sign.
Play the housetop accents as rim shots. Use the sticking of your choice— it's just the nature of this type of groove that you find your own way to do it. You might try playing the 16th notes and the tom note with your left hand, and the rest of the pattern with your right. You can experiment with accenting the 2, 4, or & of 4 to varying degrees, as well. Jackson plays the bass drum with a slight accent on 2 and 4; on the last chorus he plays the bass on 2 and 4 only. He often accents the 1 with the bass drum at the beginning of new sections, so leave yourself some dynamic room to punch that. There's no hihat on this song, but you could play it on 2 and 4 if you want to.