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OddOneRunCount on BinaryWord ​

The number of maximal runs of ones of odd length.

On BinaryWord

Called as CombinatorialStat(x, "OddOneRunCount"). 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 St000389

The number of runs of ones of odd length in a binary word.

ObjectValue
00
11
000
011
101
110
0000
0011

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000389 has the rest.