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

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.

Crossrefs

Cf. A010060.

Sequence in context: A205138 A233763 A109526 * A331118 A260723 A059214

Adjacent sequences: A309891 A309892 A309893 * A309895 A309896 A309897

Keyword

nonn

Author

Gabriel F. Lipnik, Aug 21 2019

Status

approved