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%I #25 May 31 2024 10:53:48
%S 1,0,1,220,68826306,739745383235859818
%N Number of magic squares of order n composed of the numbers from 1 to n^2, counted up to rotations, reflections, and M-transformations.
%C Chebrakov (2008) defines M-transformations of a magic square to be simultaneous permutations of its rows/columns that preserve the content of each diagonal (i.e., M-transformations can only shuffle the diagonal elements). The number of M-transformations of a magic square of order n equals A000165(floor(n/2)) = 2*A002866(floor(n/2)). Half of the M-transformations can be obtained from the other half by rotations by 180 degrees (or by reflections about a diagonal).
%C Obviously, there is no magic square for n=2, although the MATLAB command magic(n) returns a non-magic square with determinant -10. - _Altug Alkan_, Dec 25 2015
%H Yu. V. Chebrakov, <a href="http://chebrakov.narod.ru/bbb-3.1.pdf">Section 3.1.2</a> and <a href="http://chebrakov.narod.ru/bbb-3.2.pdf">Section 3.2.2</a> in "Theory of Magic Matrices. Issue TMM-1.", 2008. (in Russian)
%H Hidetoshi Mino, <a href="https://magicsquare6.net/">The number of magic squares of order 6</a>.
%F a(n) = A006052(n) / A002866(floor(n/2)).
%Y Cf. A006052.
%K nonn,hard,more
%O 1,4
%A _Max Alekseyev_, Dec 25 2015
%E a(6) from _Hidetoshi Mino_, Jul 22 2023
%E a(6) corrected by _Hidetoshi Mino_, May 31 2024
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