RowCellPairs on IntegerPartition

Pairs of cells in the same row: the sum over parts of the binomial coefficient of the part and 2.

On IntegerPartition

Called as CombinatorialStat(x, "RowCellPairs"). 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.

Sizes 1 to

FindStat St000566

The number of ways to select a row of a Ferrers shape and two cells in this row.

The number of ways to select a row of a Ferrers shape and two cells in this row. Equivalently, if $\lambda = (\lambda_0\geq\lambda_1 \geq \dots\geq\lambda_m)$ is an integer partition, then the statistic is

$$\frac{1}{2} \sum_{i=0}^m \lambda_i(\lambda_i -1).$$

Object	Value
[2]	1
[3]	3
[4]	6
[5]	10
[6]	15
[7]	21
[8]	28
[9]	36

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000566 has the rest.