[seqfan] Re: Finite cubefree words

[Kevin Ryde]

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),
0,0,0,2,2,4,4,6,2,24,12,16,54,52,88,154,144,194,436,506,714,1312

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)
2,2,6,4,10,12,14,8,54,30,44,120,130,210,360,336,476,1044,1216,1740