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RemovableHorizontalDominoes on IntegerPartition ​

Parts from which 2 can be subtracted and leave a partition: rows ending in a removable horizontal domino.

On IntegerPartition

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

Live

Distribution

Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.

FindStat St000256

The number of parts from which one can substract 2 and still get an integer partition.

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/St000256 has the rest.