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A323429
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Number of rectangular plane partitions of n.
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16
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1, 1, 3, 5, 10, 14, 26, 35, 58, 81, 124, 169, 257, 345, 501, 684, 968, 1304, 1830, 2452, 3387, 4541, 6188, 8257, 11193, 14865, 19968, 26481, 35341, 46674, 62007, 81611, 107860, 141602, 186292, 243800, 319610, 416984, 544601, 708690, 922472, 1197018, 1553442
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OFFSET
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0,3
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COMMENTS
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Number of ways to fill a (not necessarily square) matrix with the parts of an integer partition of n so that the rows and columns are weakly decreasing.
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LINKS
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EXAMPLE
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The a(5) = 14 matrices:
[5] [4 1] [3 2] [3 1 1] [2 2 1] [2 1 1 1] [1 1 1 1 1]
.
[4] [3] [2 1]
[1] [2] [1 1]
.
[3] [2]
[1] [2]
[1] [1]
.
[2]
[1]
[1]
[1]
.
[1]
[1]
[1]
[1]
[1]
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MATHEMATICA
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Table[Sum[Length[Select[Union[Sort/@Tuples[IntegerPartitions[#, {k}]&/@ptn]], And@@OrderedQ/@Transpose[#]&]], {ptn, IntegerPartitions[n]}, {k, Min[ptn]}], {n, 30}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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