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

Author

Jeffrey Shallit, Mar 09 2017

Keywords

• nonn
• more

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)).

Examples

			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.