[seqfan] Re: Finite cubefree words

Kevin Ryde user42_kevin at yahoo.com.au
Tue May 9 02:21:18 CEST 2017

njasloane at gmail.com (Neil Sloane) writes:
> Second question.  Call a binary cubefree word S a dead-end
> if both S0 and S1 contain cubes.  Meaning S can't be extended
> to a cubefree word of greater length.

Some dead-ends have a previous dead-end as a suffix.  S0 and S1 length 1
or 2 mod 3 always like that, and some new non-suffix ones at 0 mod 3.
I count new ones (but with low confidence),

I think a new one is when S0 or S1 is a kind of full cube, a cube word
like abcabcabc which is only a cube because of abc, it has no smaller
cube subword.  Is there a name for that?  I count (maybe)

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