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A321732
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Number of nonnegative integer square matrices with sum of entries equal to n, no zero rows or columns, and the same row sums as column sums.
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6
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1, 1, 3, 11, 53, 317, 2293, 19435, 188851, 2068417, 25203807, 338117445, 4951449055, 78589443061, 1343810727205, 24626270763109, 481489261372381, 10004230113283129, 220125503239710879, 5113204953106107087, 125037079246130168973
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OFFSET
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0,3
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LINKS
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EXAMPLE
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The a(3) = 11 matrices:
[3]
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[2 0] [1 1] [1 0] [0 1]
[0 1] [1 0] [0 2] [1 1]
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[1 0 0] [1 0 0] [0 1 0] [0 1 0] [0 0 1] [0 0 1]
[0 1 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [0 1 0]
[0 0 1] [0 1 0] [0 0 1] [1 0 0] [0 1 0] [1 0 0]
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MATHEMATICA
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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/@#], Total/@prs2mat[#]==Total/@Transpose[prs2mat[#]]]&]], {n, 5}]
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CROSSREFS
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Cf. A000700, A000701, A006052, A007016, A120732, A319056, A320451, A321718, A321719, A321722, A321733, A321734, A321735, A321736, A321739.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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