A283502 Number of distinct subword complexity profiles for purely periodic binary infinite words of period n.

1, 2, 2, 4, 3, 7, 6, 13, 13, 23, 25, 47, 51, 87, 110, 176, 214, 342, 424, 676, 841, 1253, 1660

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