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A323435 Number of rectangular plane partitions of n with no repeated rows or columns. 4
1, 1, 1, 3, 3, 6, 8, 13, 15, 28, 33, 52, 69, 101, 133, 202, 256, 369, 506, 688, 935, 1295, 1736, 2355, 3184, 4284, 5745, 7722, 10281, 13691, 18316, 24168, 32058, 42389, 55915, 73542, 96753, 126709, 166079, 217017, 283258 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
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 and with no repeated rows or columns.
LINKS
EXAMPLE
The a(7) = 13 plane partitions:
[7] [4 3] [5 2] [6 1] [4 2 1]
.
[6] [5] [3 2] [4 1] [4] [2 2] [3 1]
[1] [2] [1 1] [1 1] [3] [2 1] [2 1]
.
[4]
[2]
[1]
MATHEMATICA
Table[Sum[Length[Select[Union[Tuples[IntegerPartitions[#, {k}]&/@ptn]], And[UnsameQ@@#, UnsameQ@@Transpose[#], And@@(OrderedQ[#, GreaterEqual]&/@Transpose[#])]&]], {ptn, IntegerPartitions[n]}, {k, Min[ptn]}], {n, 20}]
CROSSREFS
Sequence in context: A280197 A333526 A097307 * A026804 A240213 A205970
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 15 2019
STATUS
approved

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Last modified April 22 21:44 EDT 2024. Contains 371906 sequences. (Running on oeis4.)