A297531 - OEIS

%I #6 Jan 01 2018 08:07:58

%S 1,2,4,6,10,13,17,21,24,26,30,34,38,42,45,48,50,52,56,60,64,68,72,76,

%T 80,84,87,90,93,96,98,100,102,104,108,112,116,120,124,128,132,136,140,

%U 144,148,152,156,160,164,168,171,174,177,180,183,186,189,192,194,196,198,200,202,204,206,208,212,216,220,224,228,232,236,240

%N Subword complexity (number of distinct blocks) of length n occurring in the "twisted" Thue-Morse sequence.

%C The "twisted" Thue-Morse sequence 00100110100... is the one given in A059448, but prefixed with 0.  It is the image, under the map sending 0, 2 -> 0 and 1 -> 1 of the fixed point, starting with 0, of the morphism 0 -> 02, 1 -> 21, 2 -> 12.

%C This sequence has the maximum possible subword complexity over all binary overlap-free words.

%F For n >= 4 we have a(n+1) =

%F 4n - 3*2^{i-2} for 2^i <= n <= 3*2^{i-1};

%F 3n + 3*2^{i-2} for 3*2^{i-1} <= n <= 7*2^{i-2};

%F 2n + 5*2^{i-1} for 7*2^{i-2} <= n <= 2^{i+1}.

%e For n=3 we have a(3) = 6, corresponding to the blocks 001, 010, 100, 011, 110, 101.

%Y Cf. A005942, which enumerates the same thing for the ordinary Thue-Morse sequence A010060.

%K nonn

%O 0,2

%A _Jeffrey Shallit_, Dec 31 2017