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

0,4

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

Table of n, a(n) for n=0..40.

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

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

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

Sequence in context: A280197 A333526 A097307 * A026804 A240213 A205970

Adjacent sequences: A323432 A323433 A323434 * A323436 A323437 A323438

Keyword

nonn

Author

Gus Wiseman, Jan 15 2019

Status

approved