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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. 12
1, 0, 9, 68688, 579043051200, 94590660245399996601600 (list; graph; refs; listen; history; text; internal format)



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.

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


Table of n, a(n) for n=1..6.

Artem Ripatti, On the number of semi-magic squares of order 6, arXiv:1807.02983 [math.CO], 2018. See Table 1 p. 2.

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.


a(n) = A271104(n)* n^2.


Cf. A006052, A270876, A271104.

Sequence in context: A321581 A053971 A013790 * A058452 A058456 A184991

Adjacent sequences:  A271100 A271101 A271102 * A271104 A271105 A271106




William Walkington, Mar 30 2016


a(6) added by William Walkington, Jul 17 2018



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Last modified October 20 13:54 EDT 2020. Contains 337904 sequences. (Running on oeis4.)