|
|
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
|
|
|
|
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
|
|
|
FORMULA
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,hard,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|