A323530 Number of square plane partitions of n with strictly decreasing rows and columns.

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 5, 8, 10, 15, 18, 25, 30, 39, 46, 58, 67, 82, 94, 112, 127, 149, 168, 194, 218, 251, 282, 324, 368, 425, 489, 573, 670, 797, 952, 1148, 1392, 1703, 2086, 2568, 3168, 3908, 4823, 5947, 7318, 8986, 11012, 13443, 16371, 19866

Offset: 0

Author

Gus Wiseman, Jan 17 2019

Keywords

• nonn

Examples

			The a(12) = 8 plane partitions:
  [12]
.
  [5 4] [6 3] [7 2] [5 3] [6 2] [4 3] [5 2]
  [2 1] [2 1] [2 1] [3 1] [3 1] [3 2] [4 1]
		

Crossrefs

Cf. A000219, A089299, A306320, A323429, A323434, A323439, A323522, A323529, A323530, A323531.

Programs

Mathematica

Table[Sum[Length[Select[Tuples[IntegerPartitions[#,{Length[ptn]}]&/@ptn],And@@Greater@@@#&&And@@Greater@@@Transpose[#]&]],{ptn,IntegerPartitions[n]}],{n,30}]