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A283502 Number of distinct subword complexity profiles for purely periodic binary infinite words of period n. 0
1, 2, 2, 4, 3, 7, 6, 13, 13, 23, 25, 47, 51, 87, 110, 176, 214, 342, 424, 676, 841, 1253, 1660 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The subword complexity function p_i(x) maps i to the number of distinct contiguous blocks (aka subwords, aka factors) of length i in an infinite word x. The subword complexity profile of an infinite word x is the infinite list (p_1 (x), p_2 (x), p_3 (x), ...).   For a purely periodic infinite word x, of period n, it suffices to consider the finite list (p_1 (x), p_2 (x), ..., p_n (x)).  Furthermore, if x = www... with w of length n, it suffices to consider the list (p_1 (ww), p_2 (ww), ..., p_n (ww)).

LINKS

Table of n, a(n) for n=1..23.

EXAMPLE

For period n = 5, there are exactly three distinct subword complexity profiles:  (1,1,1,...) corresponding to the word 000...; (2,3,4,5,5,5,...) corresponding to the word 000010000100001...; and

(2,4,5,5,5,...) corresponding to the word 000110001100011... .

CROSSREFS

Cf. A282949.

Sequence in context: A238779 A239832 A240010 * A324756 A324754 A174220

Adjacent sequences:  A283499 A283500 A283501 * A283503 A283504 A283505

KEYWORD

nonn,more

AUTHOR

Jeffrey Shallit, Mar 09 2017

STATUS

approved

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Last modified September 21 08:38 EDT 2020. Contains 337268 sequences. (Running on oeis4.)