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A266237
Number of magic squares of order n composed of the numbers from 1 to n^2, counted up to rotations, reflections, and M-transformations.
0
1, 0, 1, 220, 68826306, 739745383235859818
OFFSET
1,4
COMMENTS
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).
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
LINKS
Yu. V. Chebrakov, Section 3.1.2 and Section 3.2.2 in "Theory of Magic Matrices. Issue TMM-1.", 2008. (in Russian)
FORMULA
a(n) = A006052(n) / A002866(floor(n/2)).
CROSSREFS
Cf. A006052.
Sequence in context: A091756 A167825 A339680 * A371899 A159565 A330281
KEYWORD
nonn,hard,more
AUTHOR
Max Alekseyev, Dec 25 2015
EXTENSIONS
a(6) from Hidetoshi Mino, Jul 22 2023
a(6) corrected by Hidetoshi Mino, May 31 2024
STATUS
approved