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A006052 Number of magic squares of order n composed of the numbers from 1 to n^2, counted up to rotations and reflections.
(Formerly M5482)

%I M5482

%S 1,0,1,880,275305224

%N Number of magic squares of order n composed of the numbers from 1 to n^2, counted up to rotations and reflections.

%C a(4) computed by Frenicle de Bessy (1605 ? - 1675), published in 1693. The article mentions the 880 squares and considers also 5*5, 6*6, 8*8, and other squares. - _Paul Curtz_, Jul 13 and Aug 12 2011

%C a(5) computed by Richard C. Schroeppel in 1973.

%C According to Pinn and Wieczerkowski, a(6) = (0.17745 +- 0.00016) * 10^20. - _R. K. Guy_, May 01 2004

%D E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Vol. II, pp. 778-783 gives the 880 4 X 4 squares.

%D M. Gardner, Mathematical Games, Sci. Amer. Vol. 249 (No. 1, 1976), p. 118.

%D M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 216.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Ian Cameron, Adam Rogers and Peter Loly, <a href="http://www.physics.umanitoba.ca/~icamern/Poland2012/Data/Bewedlo%20Codex.pdf">"The Library of Magical Squares" -- a summary of the main results for the Shannon entropy of magic and Latin squares: isentropic clans and indexing, in celebration of George Styan's 75th</a>.

%H Frenicle de Bessy, <a href="http://babel.hathitrust.org/cgi/pt?u=1&amp;num=423&amp;seq=11&amp;view=image&amp;size=100&amp;id=ucm.5323750390">Des carrez ou tables magiques</a>, Divers ouvrages de mathematique et de physique (1693), pp. 423-483.

%H Frenicle de Bessy, <a href="http://babel.hathitrust.org/cgi/pt?u=1&amp;num=484&amp;seq=9&amp;view=image&amp;size=100&amp;id=ucm.5323750390">Table générale des carrez de quatre</a>, Divers ouvrages de mathematique et de physique (1693), pp. 484-503.

%H I. Peterson, <a href="http://www.maa.org/mathland/mathtrek_10_18_99.html">Magic Tesseracts</a> [Broken link?]

%H K. Pinn and C. Wieczerkowski, <a href="http://www.arXiv.org/abs/cond-mat/9804109">Number of magic squares from parallel tempering Monte Carlo</a>, Internat. J. Modern Phys., 9 (4) (1998) 541-546.

%H Artem Ripatti, <a href="https://arxiv.org/abs/1807.02983">On the number of semi-magic squares of order 6</a>, arXiv:1807.02983 [math.CO], 2018. See Table 1 p. 2.

%H R. Schroeppel, <a href="/A006052/a006052_2.pdf">Emails to N. J. A. Sloane, Jun. 1991</a>

%H N. J. A. Sloane & J. R. Hendricks, <a href="/A006052/a006052_3.pdf">Correspondence, 1974</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MagicSquare.html">Magic Square</a>

%H <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>

%e An illustration of the unique (up to rotations and reflections) magic square of order 3:

%e +---+---+---+

%e | 2 | 7 | 6 |

%e +---+---+---+

%e | 9 | 5 | 1 |

%e +---+---+---+

%e | 4 | 3 | 8 |

%e +---+---+---+

%Y Cf. A270876, A271103, A271104.

%K nonn,hard,nice,more

%O 1,4

%A _N. J. A. Sloane_

%E Definition corrected by _Max Alekseyev_, Dec 25 2015

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Last modified August 21 22:52 EDT 2018. Contains 313958 sequences. (Running on oeis4.)