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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.
5
1, 1, 1, 13, 13, 45, 681, 885, 2805, 8301, 237213
OFFSET
0,4
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}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 15 2018
STATUS
approved