A321645 Number of distinct row/column permutations of plane partitions of n.

1, 1, 3, 11, 32, 96, 290, 864, 2502, 7134, 20081

Offset

0,3

Links

Table of n, a(n) for n=0..10.

Example

The a(3) = 11 permutations of plane partitions:
  [3] [2 1] [1 2] [1 1 1]
.
  [2] [1 1] [1 1] [1] [1 0] [0 1]
  [1] [1 0] [0 1] [2] [1 1] [1 1]
.
  [1]
  [1]
  [1]

Mathematica

submultisetQ[M_, N_]:=Or[Length[M]==0, MatchQ[{Sort[List@@M], Sort[List@@N]}, {{x_, Z___}, {___, x_, W___}}/; submultisetQ[{Z}, {W}]]];
multsubs[set_, k_]:=If[k==0, {{}}, Join@@Table[Prepend[#, set[[i]]]&/@multsubs[Drop[set, i-1], k-1], {i, Length[set]}]];
Table[Length[Select[multsubs[Tuples[Range[n], 2], n], And[Union[First/@#]==Range[Max@@First/@#], Union[Last/@#]==Range[Max@@Last/@#], OrderedQ[Sort[Map[Last, GatherBy[Sort[Reverse/@#], First], {2}], submultisetQ], submultisetQ], OrderedQ[Sort[Sort/@Map[Last, GatherBy[#, First], {2}], submultisetQ], submultisetQ]]&]], {n, 6}]

Crossrefs

Cf. A000219, A001970, A007716, A008480, A068313, A114736, A120733, A316983, A319646.

Cf. A321646, A321647, A321648, A321652, A321653, A321655.

Sequence in context: A110958 A141211 A353065 * A296315 A125671 A034561

Adjacent sequences: A321642 A321643 A321644 * A321646 A321647 A321648

Keyword

nonn,more

Author

Gus Wiseman, Nov 15 2018

Status

approved