A321653 Number of nonnegative integer matrices with sum of entries equal to n and no zero rows or columns, with strictly decreasing row sums and column sums.

1, 1, 1, 5, 5, 14, 44, 72, 147, 381, 1405

Offset

0,4

Links

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

Example

The a(5) = 14 matrices:
  [5] [4 1] [3 2]
.
  [4] [4 0] [3 1] [3 1] [3] [3 0] [3 0] [2 2] [2 1] [2 1] [1 2]
  [1] [0 1] [1 0] [0 1] [2] [1 1] [0 2] [1 0] [2 0] [1 1] [2 0]

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/@#], OrderedQ[Total/@prs2mat[#], Greater], OrderedQ[Total/@Transpose[prs2mat[#]], Greater]]&]], {n, 6}]

Crossrefs

Cf. A000219, A001970, A007716, A068313, A114736, A117433, A120733, A319646, A321645, A321652, A321654, A321655.

Sequence in context: A317617 A294750 A304300 * A247940 A061200 A255304

Adjacent sequences: A321650 A321651 A321652 * A321654 A321655 A321656

Keyword

nonn,more

Author

Gus Wiseman, Nov 15 2018

Status

approved