extending sequences, A046858 and A088532

[Joshua Zucker]

I would love to extend A046858 -- it sounds pretty! -- but I have no
idea what the "strength" of a relation is.  Can anyone help?

I have also been extending A088532 by brute force... Any ideas about
how to do it better?

--Joshua Zucker

A088532, max # of patterns, and all permutations (up to reversal) that
attain the max.
1: (1)
2: (12)
4: (132) (213)
8: (2413)
15: (25314)
28: (253614) (264153) (361425) (426315)
55: (2574163) (3614725) (3624715) (3714625) (5274136)
109: (25836147) (36185274) (38527416) (52741836)