Dear all, I'm not a good looker, but I didn't find either of the sequences 0,1,3,11,39,139,495,... 0,1,3,5,3,-11,-45,-91,... in OEIS. There still seems to be room for a few hundred more divisibility sequences satisfying second order recurrences. Many of them count combinatorial objects. I'm sorry that I don't have the expertise to submit them myself. R.