OFFSET
0,4
EXAMPLE
The a(6) = 9 permutations of strict plane partitions:
[6] [2 4] [4 2] [1 5] [5 1] [1 2 3] [1 3 2] [2 1 3] [2 3 1] [3 1 2] [3 2 1]
.
[1] [5] [0 1] [1 0] [2 3] [3 2] [2] [4] [0 2] [1 3] [2 0] [3 1]
[5] [1] [2 3] [3 2] [0 1] [1 0] [4] [2] [1 3] [0 2] [3 1] [2 0]
.
[1] [1] [2] [2] [3] [3]
[2] [3] [1] [3] [1] [2]
[3] [2] [3] [1] [2] [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/@#], UnsameQ@@Length/@Split[#], OrderedQ[Sort[Map[Last, GatherBy[Sort[Reverse/@#], First], {2}], submultisetQ], submultisetQ], OrderedQ[Sort[Sort/@Map[Last, GatherBy[#, First], {2}], submultisetQ], submultisetQ]]&]], {n, 5}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 15 2018
STATUS
approved