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A309894

Number of unbordered factors of length n in the Thue-Morse sequence A010060.

1, 2, 2, 4, 2, 4, 6, 0, 4, 4, 4, 4, 12, 0, 4, 4, 8, 4, 8, 0, 8, 4, 4, 8, 24, 0, 4, 4, 8, 4, 8, 4, 16, 4, 4, 4, 16, 0, 4, 8, 16, 4, 12, 0, 8, 8, 8, 16, 48, 0, 4, 4, 8, 4, 8, 4, 16, 4, 8, 4, 16, 4, 8, 12, 32, 4, 8, 0, 8, 4, 4, 12, 32, 0, 8, 4, 8, 8, 12, 8, 32

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OFFSET

0,2

COMMENTS

a(n) <= n for n >= 4 with a(n) = n infinitely often.

This sequence is 2-regular.

LINKS

Gabriel F. Lipnik, Table of n, a(n) for n = 0..99999

D. Goč, H. Mousavi and J. Shallit, On the number of unbordered factors, arXiv:1211.1301 [cs.FL], 2012.

D. Goč, H. Mousavi and J. Shallit, On the number of unbordered factors, Language and automata theory and applications, Springer, 2013, 299-310.

EXAMPLE

For n = 3 the a(3) = 4 unbordered factors of length 3 in A010060 are 001, 011, 100 and 110.