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PartsExceedingOnes on IntegerPartition ​

Parts larger than the number of parts equal to 1.

On IntegerPartition

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

Live

FindStat St000473

The number of parts of a partition that are strictly bigger than the number of ones.

ObjectValue
[]0
[1]0
[2]1
[3]1
[4]1
[5]1
[6]1
[7]1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000473 has the rest.