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A271103 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. 3
1, 0, 9, 68688, 579043051200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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]

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 hosted by Math Forum at Drexel University.

The number of order 5 magic and semi-magic squares was computed by Walter Trump in March 2000.

LINKS

Table of n, a(n) for n=1..5.

Mutsumi Suzuki, Magic Squares, hosted by Math Forum at Drexel University.

Walter Trump, How many magic squares are there? - Results of historical and computer enumeration.

FORMULA

a(n) = A271104(n)* n^2. - William Walkington, Apr 11 2016

CROSSREFS

Cf. A006052, A270876, A271104.

Sequence in context: A159398 A053971 A013790 * A058452 A058456 A014381

Adjacent sequences:  A271100 A271101 A271102 * A271104 A271105 A271106

KEYWORD

nonn,more

AUTHOR

William Walkington, Mar 30 2016

STATUS

approved

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.