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%I #57 Sep 06 2023 21:19:22
%S 1,0,9,68688,579043051200,94590660245399996601600
%N Number of magic and semi-magic squares of order n composed of the numbers from 1 to n^2, counted up to rotations and reflections.
%C A semi-magic square differs from a magic square in that at least one of its main diagonals does not sum to the magic constant. [_Walter Trump_]
%C The number of order 4 magic and semi-magic squares was computed by Mutsumi Suzuki, and could be found on his former web site. Mutsumi Suzuki's pages are now in the Internet Archive.
%C The number of order 5 magic and semi-magic squares was computed by _Walter Trump_ in March 2000.
%C The number of order 6 magic and semi-magic squares was calculated by Artem Ripatti in April 2018, and published in his paper dated July 10, 2018. - _William Walkington_, Jul 17 2018
%H Artem Ripatti, <a href="https://arxiv.org/abs/1807.02983">On the number of semi-magic squares of order 6</a>, arXiv:1807.02983 [math.CO], 2018. See Table 1 p. 2.
%H Mutsumi Suzuki, <a href="https://web.archive.org/web/20011115233406/http://www.pse.che.tohoku.ac.jp/~msuzuki/MagicSquare.4x4.semi.html">Semi-Magic Squares of 4 x 4</a>, first "captured" by the Internet Archive on the 5th October 1999.
%H Walter Trump, <a href="http://www.trump.de/magic-squares/howmany.html">How many magic squares are there? - Results of historical and computer enumeration</a>.
%F a(n) = A271104(n)* n^2.
%Y Cf. A006052, A270876, A271104.
%K nonn,more
%O 1,3
%A _William Walkington_, Mar 30 2016
%E a(6) added by _William Walkington_, Jul 17 2018
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