OFFSET
0,4
COMMENTS
If these partitions are "flattened" into a simple partition, the resulting partitions are those for which any part size present with multiplicity k implies the presence of at least k(k-1)/2 larger parts. E.g., [3,1|1] flattens to [3,1^2], 1 has multiplicity 2, so there must be at least 2*1/2 = 1 part larger than 1 - which is the 3.
REFERENCES
B. Gordon, Multirowed partitions with strict decrease along columns (Notes on plane partitions IV.), Symposia Amer. Math. Soc. 19 (1971) 91-100.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..85
EXAMPLE
For n = 5, we have the 6 partitions [5], [4,1], [4|1], [3,2], [3|2] and [3,1|1].
CROSSREFS
KEYWORD
nonn
AUTHOR
Franklin T. Adams-Watters, Mar 16 2006
EXTENSIONS
Clarified definition, added 30 terms and reference. - Dennis K Moore, Jan 12 2011
a(40)-a(44) from Alois P. Heinz, Sep 26 2018
STATUS
approved