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.