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A323432
Number of semistandard rectangular plane partitions of n.
7
1, 1, 2, 4, 6, 9, 15, 20, 30, 42, 59, 79, 112, 146, 199, 264, 350, 455, 603, 774, 1010, 1297, 1668, 2124, 2724, 3441, 4372, 5513, 6955, 8718, 10960, 13670, 17091, 21264, 26454, 32786, 40667, 50215, 62048, 76435, 94126
OFFSET
0,3
COMMENTS
Number of ways to fill a (not necessarily square) matrix with the parts of an integer partition of n so that the rows are weakly decreasing and the columns are strictly decreasing.
EXAMPLE
The a(6) = 15 matrices:
[6] [51] [42] [411] [33] [321] [3111] [222] [2211] [21111] [111111]
.
[5] [4] [22]
[1] [2] [11]
.
[3]
[2]
[1]
MATHEMATICA
Table[Sum[Length[Select[Union[Tuples[IntegerPartitions[#, {k}]&/@ptn]], And@@(OrderedQ[#, Greater]&/@Transpose[#])&]], {ptn, IntegerPartitions[n]}, {k, Min[ptn]}], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 16 2019
STATUS
approved