I still don't know what you mean by n ≤ 10.
Have you played around with the demo?
http://recur-env.eba-rm3fchmn.us-east-2.elasticbeanstalk.com...
You can input there a sequence and it will predict the expression and next elements.
For example, for the sequence: [3, 1, 8, 9, 18, 19, 37, 74, 92, 166, 332, 406, 738, 1476]
It predicts: u_n = u_(n−1) + (u_(n−3) (n mod 3)) + u_(n−4)
It's a really decent guess, and if I give it one more element (from 14 to 15 elements) it gets it correctly.