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BulgarianSolitairePreimageCount on IntegerPartition ​

The partitions of the same size that Bulgarian solitaire (remove the first column, insert it as a row) sends to this one: the distinct part sizes of at least the number of parts less one.

On IntegerPartition

Called as CombinatorialStat(x, "BulgarianSolitairePreimageCount"). 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 St001913

The number of preimages of an integer partition in Bulgarian solitaire.

ObjectValue
[1]1
[2]1
[3]1
[4]1
[5]1
[6]1
[7]1
[8]1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001913 has the rest.