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Number of length-n binary words whose subword complexity is bounded by 2i for 1<=i<=n, and containing no blocks of exponent > 5/2.
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%I #7 Jul 02 2024 03:00:45

%S 1,2,4,6,10,16,24,36,50,72,102,142,194,240,298,362,434,504,528,570,

%T 624,668,712,738,778,806,810,844,836,800,806,826,844,834,844,848,812,

%U 828,864,900,916,912,900,822,786,766,736,740,766,776,780,788,808,836,864

%N Number of length-n binary words whose subword complexity is bounded by 2i for 1<=i<=n, and containing no blocks of exponent > 5/2.

%C The exponent of a word is defined to be its length divided by its shortest period. For example, "alfalfa" has exponent 7/3. Subword complexity is the number of distinct length-n blocks.

%H Nicolas Ollinger and Jeffrey Shallit, <a href="https://arxiv.org/abs/2406.17867">The repetition threshold for Rote sequences</a>, Arxiv preprint arXiv:2406.17867 [math.CO], June 25 2024.

%Y Cf. A285894.

%K nonn

%O 0,2

%A _Jeffrey Shallit_, Jun 28 2024