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A114736 revision #17


A114736
Number of planar partitions of n where parts strictly decrease along each row and column.
27
1, 1, 1, 3, 4, 6, 10, 15, 22, 33, 49, 70, 102, 146, 205, 290, 405, 561, 779, 1071, 1463, 1999, 2714, 3667, 4946, 6641, 8880, 11848, 15753, 20870, 27586, 36354, 47766, 62621, 81878, 106785, 138975, 180449, 233778, 302270, 390027, 502256, 645603, 828330, 1060851
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
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
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