HalfPerimeter on IntegerPartition
Half the perimeter of the bounding rectangle of the Young diagram: largest part plus number of parts.
FindStat's St000459 calls the hook length of the base cell the perimeter; that is HookLengthOfFirstCell, one less than this.
Called as CombinatorialStat(x, "HalfPerimeter"). The head's page has its examples.
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Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.