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A297531 Subword complexity (number of distinct blocks) of length n occurring in the "twisted" Thue-Morse sequence. 1
1, 2, 4, 6, 10, 13, 17, 21, 24, 26, 30, 34, 38, 42, 45, 48, 50, 52, 56, 60, 64, 68, 72, 76, 80, 84, 87, 90, 93, 96, 98, 100, 102, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

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

LINKS

Table of n, a(n) for n=0..73.

FORMULA

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

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

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

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

EXAMPLE

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

CROSSREFS

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

Sequence in context: A233349 A233556 A087148 * A334821 A275489 A153817

Adjacent sequences:  A297528 A297529 A297530 * A297532 A297533 A297534

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Dec 31 2017

STATUS

approved

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Last modified August 9 18:55 EDT 2022. Contains 356026 sequences. (Running on oeis4.)