[seqfan] Number of binary privileged words, etc

[Neil Sloane]

Dear Sequence Fans,
This paper:

Gabriele Fici, Open and Closed Words, in Giovanni Pighizzini, ed., The
Formal Language Theory Column, Bulletin of EATCS, 2017,
http://bulletin.eatcs.org/index.php/beatcs/article/viewFile/508/497

discusses open words (A297183), closed words (A226452), and
privileged words (A231208)

The author also mentions that

" a privileged word is always closed, but there exist closed words that are
not privileged, e.g. abab, ababab, ababbabab, etc."

What is the number of closed words of length n that are not privileged ?