A323435 Number of rectangular plane partitions of n with no repeated rows or columns.

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

Offset: 0

Author

Gus Wiseman, Jan 15 2019

Keywords

• nonn

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.

Examples

			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]
		

Crossrefs

Cf. A000219, A003293, A047966, A101509, A114736, A117433, A299968, A319066.

Cf. A323301, A323307, A323429, A323430, A323431, A323432, A323436, A323438.

Programs

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}]