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 A321722 Number of non-normal magic squares whose entries are nonnegative integers summing to n. 13
 1, 1, 1, 1, 10, 21, 97, 657, 5618, 48918, 494530, 5383553, 65112565, 840566081, 11834555867, 176621056393, 2838064404989, 48060623405313 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS 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. LINKS Wikipedia, Magic square FORMULA a(p) = A007016(p) + 1 if p is prime. a(n) >= A007016(n) + 1 for n > 1. - Chai Wah Wu, Jan 15 2019 EXAMPLE The a(4) = 10 magic squares:   [4] .   [1 1]   [1 1] .   [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] 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/@#], SameQ@@Join[{Tr[prs2mat[#]], Tr[Reverse[prs2mat[#]]]}, Total/@prs2mat[#], Total/@Transpose[prs2mat[#]]]]&]], {n, 5}] CROSSREFS Cf. A006052, A007016, A120732, A271103, A319056, A319616. Cf. A321718, A321719, A321720, A321721. Sequence in context: A082669 A215574 A146083 * A306208 A001739 A072805 Adjacent sequences:  A321719 A321720 A321721 * A321723 A321724 A321725 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 18 2018 EXTENSIONS a(7)-a(15) from Chai Wah Wu, Jan 15 2019 a(16)-a(17) from Chai Wah Wu, Jan 16 2019 STATUS approved

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Last modified August 4 10:11 EDT 2021. Contains 346447 sequences. (Running on oeis4.)