FirstRowHookLengthSum on IntegerPartition
The sum of the hook lengths in the first row: the size plus the binomial of the largest part and 2.
Called as CombinatorialStat(x, "FirstRowHookLengthSum"). 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 St000867
The sum of the hook lengths in the first row of an integer partition.
| Object | Value |
|---|---|
[] | 0 |
[1] | 1 |
[2] | 3 |
[3] | 6 |
[4] | 10 |
[5] | 15 |
[6] | 21 |
[7] | 28 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000867 has the rest.