A321654 Number of nonnegative integer matrices with sum of entries equal to n and no zero rows or columns, with distinct row sums and distinct column sums.

1, 1, 1, 13, 13, 45, 681, 885, 2805, 8301, 237213

Offset

0,4

Links

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

Example

The a(3) = 13 matrices:
  [3] [2 1] [1 2]
.
  [2] [2 0] [1 1] [1 1] [1] [1 0] [1 0] [0 2] [0 1] [0 1]
  [1] [0 1] [1 0] [0 1] [2] [1 1] [0 2] [1 0] [2 0] [1 1]

Mathematica

prs2mat[prs_]:=Table[Count[prs, {i, j}], {i, Union[First/@prs]}, {j, Union[Last/@prs]}];
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@@Total/@prs2mat[#], UnsameQ@@Total/@Transpose[prs2mat[#]]]&]], {n, 5}]

Crossrefs

Cf. A000219, A001970, A007716, A068313, A114736, A117433, A120733, A319646, A321645, A321646, A321652.

Sequence in context: A214466 A302678 A147249 * A302513 A147013 A147187

Adjacent sequences: A321651 A321652 A321653 * A321655 A321656 A321657

Keyword

nonn,more

Author

Gus Wiseman, Nov 15 2018

Status

approved