

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)


11




OFFSET

1,4


COMMENTS

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
a(5) computed by Richard C. Schroeppel in 1973.
According to Pinn and Wieczerkowski, a(6) = (0.17745 + 0.00016) * 10^20.  R. K. Guy, May 01 2004


REFERENCES

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Vol. II, pp. 778783 gives the 880 4 X 4 squares.
M. Gardner, Mathematical Games, Sci. Amer. Vol. 249 (No. 1, 1976), p. 118.
M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 216.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=1..5.
Ian Cameron, Adam Rogers and Peter Loly, "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.
Frenicle de Bessy, Des carrez ou tables magiques, Divers ouvrages de mathematique et de physique (1693), pp. 423483.
Frenicle de Bessy, Table générale des carrez de quatre, Divers ouvrages de mathematique et de physique (1693), pp. 484503.
I. Peterson, Magic Tesseracts [Broken link?]
K. Pinn and C. Wieczerkowski, Number of magic squares from parallel tempering Monte Carlo, Internat. J. Modern Phys., 9 (4) (1998) 541546.
R. Schroeppel, Emails to N. J. A. Sloane, Jun. 1991
N. J. A. Sloane & J. R. Hendricks, Correspondence, 1974
Eric Weisstein's World of Mathematics, Magic Square
Index entries for sequences related to magic squares


EXAMPLE

An illustration of the unique (up to rotations and reflections) magic square of order 3:
++
 2  7  6 
++
 9  5  1 
++
 4  3  8 
++


CROSSREFS

Cf. A270876, A271103, A271104.
Sequence in context: A118799 A206341 A024393 * A105976 A265181 A137064
Adjacent sequences: A006049 A006050 A006051 * A006053 A006054 A006055


KEYWORD

nonn,hard,nice,more


AUTHOR

N. J. A. Sloane


EXTENSIONS

Definition corrected by Max Alekseyev, Dec 25 2015


STATUS

approved



