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A321722
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Number of non-normal magic squares whose entries are nonnegative integers summing to n.
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13
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1, 1, 1, 1, 10, 21, 97, 657, 5618, 48918, 494530, 5383553, 65112565, 840566081, 11834555867, 176621056393, 2838064404989, 48060623405313
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OFFSET
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0,5
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COMMENTS
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A non-normal magic square is a square matrix with row sums, column sums, and both diagonals all equal to d, for some d|n.
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LINKS
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FORMULA
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EXAMPLE
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The a(4) = 10 magic squares:
[4]
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[1 1]
[1 1]
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[1 0 0 0][1 0 0 0][0 1 0 0][0 1 0 0][0 0 1 0][0 0 1 0][0 0 0 1][0 0 0 1]
[0 0 1 0][0 0 0 1][0 0 1 0][0 0 0 1][1 0 0 0][0 1 0 0][1 0 0 0][0 1 0 0]
[0 0 0 1][0 1 0 0][1 0 0 0][0 0 1 0][0 1 0 0][0 0 0 1][0 0 1 0][1 0 0 0]
[0 1 0 0][0 0 1 0][0 0 0 1][1 0 0 0][0 0 0 1][1 0 0 0][0 1 0 0][0 0 1 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/@#], SameQ@@Join[{Tr[prs2mat[#]], Tr[Reverse[prs2mat[#]]]}, Total/@prs2mat[#], Total/@Transpose[prs2mat[#]]]]&]], {n, 5}]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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