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OnePositionSum on BinaryWord ​

The sum of the positions of the ones.

On BinaryWord

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

Live

Distribution

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

FindStat St000391

The sum of the positions of the ones in a binary word.

ObjectValue
00
11
000
012
101
113
0000
0013

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000391 has the rest.