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DistinctSquareCount on BinaryWord ​

The distinct nonempty words u with uu a factor.

On BinaryWord

FindStat's St001424.

Called as CombinatorialStat(x, "DistinctSquareCount"). The head's page has its examples.

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Distribution

Over BinaryWords at each size, tallied here in your browser; sizes past 6 are not offered.

FindStat St001424

The number of distinct squares in a binary word.

ObjectValue
00
10
001
010
100
111
0001
0011

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001424 has the rest.