A343484 Number of equivalence classes of length n squarefree reduced words over {0, 1, 2, 3} under action of renaming symbols.
0, 1, 1, 2, 3, 5, 8, 13, 18, 27, 41, 62, 90, 134, 198, 293, 423, 619, 908, 1329, 1938, 2832, 4142, 6061, 8824, 12879, 18794, 27425, 39977, 58333, 85109, 124180, 180994, 263931, 384933, 561402, 818617, 1193841, 1740980, 2538896, 3702022, 5398458, 7872351
Offset: 0
Keywords
Examples
a(5) = 5 corresponds to the 5 words 01210, 01030, 01230, 01032, and 01232.
Links
- Richard A. Dean, A sequence without repeats on x, x^{-1}, y, y^{-1}, Amer. Math. Monthly 72, 1965. pp. 383-385. MR 31 #350.
- Tero Harju, Avoiding Square-Free Words on Free Groups, arXiv:2104.06837 [math.CO], 2021.
Formula
a(n) = A343421(n)/8 for n >= 2.
Comments