DistinctEvenSubsetSums on IntegerPartition
Distinct nonzero even sums of sub-multisets of the parts.
Follows FindStat's Sage code and its data, not its title: the "partial sums" it counts are the sums of arbitrary sub-multisets of the parts (the code runs over all subsets), not of the running prefixes. The empty sum, 0, is not counted.
Called as CombinatorialStat(x, "DistinctEvenSubsetSums"). 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 St000547
The number of even non-empty partial sums of an integer partition.
| Object | Value |
|---|---|
[] | 0 |
[1] | 0 |
[2] | 1 |
[3] | 0 |
[4] | 1 |
[5] | 0 |
[6] | 1 |
[7] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000547 has the rest.