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.

1, 0, 9, 68688, 579043051200, 94590660245399996601600

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 in the Internet Archive.

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

Links

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, Semi-Magic Squares of 4 x 4, first "captured" by the Internet Archive on the 5th October 1999.

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

Index entries for sequences related to magic squares

Formula

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

Crossrefs

Cf. A006052, A270876, A271104.

Sequence in context: A321581 A053971 A013790 * A058452 A058456 A184991

Adjacent sequences: A271100 A271101 A271102 * A271104 A271105 A271106

Keyword

nonn,more

Author

William Walkington, Mar 30 2016

Extensions

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

Status

approved