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Number of equivalence classes of length n squarefree reduced words over {0, 1, 2, 3} under action of renaming symbols.
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%I #13 Apr 17 2021 14:31:11

%S 0,1,1,2,3,5,8,13,18,27,41,62,90,134,198,293,423,619,908,1329,1938,

%T 2832,4142,6061,8824,12879,18794,27425,39977,58333,85109,124180,

%U 180994,263931,384933,561402,818617,1193841,1740980,2538896,3702022,5398458,7872351

%N Number of equivalence classes of length n squarefree reduced words over {0, 1, 2, 3} under action of renaming symbols.

%C Any equivalence class of words with length at least 2 has exactly 8 members.

%H Richard A. Dean, <a href="http://www.jstor.org/stable/2313498">A sequence without repeats on x, x^{-1}, y, y^{-1}</a>, Amer. Math. Monthly 72, 1965. pp. 383-385. MR 31 #350.

%H Tero Harju, <a href="https://arxiv.org/abs/2104.06837">Avoiding Square-Free Words on Free Groups</a>, arXiv:2104.06837 [math.CO], 2021.

%F a(n) = A343421(n)/8 for n >= 2.

%e a(5) = 5 corresponds to the 5 words 01210, 01030, 01230, 01032, and 01232.

%Y Cf. A215075, A343421.

%K nonn

%O 0,4

%A _James Rayman_, Apr 16 2021