A309894 - OEIS

%I #24 Oct 23 2019 14:10:40

%S 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,

%T 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,

%U 12,32,4,8,0,8,4,4,12,32,0,8,4,8,8,12,8,32

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

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

%C This sequence is 2-regular.

%H Gabriel F. Lipnik, <a href="/A309894/b309894.txt">Table of n, a(n) for n = 0..99999</a>

%H D. Goč, H. Mousavi and J. Shallit, <a href="https://arxiv.org/abs/1211.1301">On the number of unbordered factors</a>, arXiv:1211.1301 [cs.FL], 2012.

%H D. Goč, H. Mousavi and J. Shallit, <a href="https://doi.org/10.1007/978-3-642-37064-9_27">On the number of unbordered factors</a>, Language and automata theory and applications, Springer, 2013, 299-310.

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

%Y Cf. A010060.

%K nonn

%O 0,2

%A _Gabriel F. Lipnik_, Aug 21 2019