A323432 Number of semistandard rectangular plane partitions of n.

1, 1, 2, 4, 6, 9, 15, 20, 30, 42, 59, 79, 112, 146, 199, 264, 350, 455, 603, 774, 1010, 1297, 1668, 2124, 2724, 3441, 4372, 5513, 6955, 8718, 10960, 13670, 17091, 21264, 26454, 32786, 40667, 50215, 62048, 76435, 94126

Offset

0,3

Comments

Number of ways to fill a (not necessarily square) matrix with the parts of an integer partition of n so that the rows are weakly decreasing and the columns are strictly decreasing.

Links

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

Example

The a(6) = 15 matrices:
  [6] [51] [42] [411] [33] [321] [3111] [222] [2211] [21111] [111111]
.
  [5] [4] [22]
  [1] [2] [11]
.
  [3]
  [2]
  [1]

Mathematica

Table[Sum[Length[Select[Union[Tuples[IntegerPartitions[#, {k}]&/@ptn]], And@@(OrderedQ[#, Greater]&/@Transpose[#])&]], {ptn, IntegerPartitions[n]}, {k, Min[ptn]}], {n, 30}]

Crossrefs

Cf. A000219, A003293, A047966, A089299, A101509, A114736, A117433, A299968, A319066.

Cf. A323301, A323307, A323429, A323430, A323431, A323435, A323436, A323438.

Sequence in context: A299494 A306597 A127740 * A327046 A024787 A266648

Adjacent sequences: A323429 A323430 A323431 * A323433 A323434 A323435

Keyword

nonn

Author

Gus Wiseman, Jan 16 2019

Status

approved