

A006052


Number of different magic squares of order n that can be formed from the numbers 1, ..., n^2.
(Formerly M5482)


4




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 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.
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 Styanís 75th", http://www.physics.umanitoba.ca/~icamern/Poland2012/Data/Bewedlo%20Codex.pdf.From N. J. A. Sloane, Dec 24 2012
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.
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
K. Pinn and C. Wieczerkowski, Number of magic squares from parallel tempering Monte Carlo, Internat. J. Modern Phys., 9 (4) (1998) 541546.
Eric Weisstein's World of Mathematics, Magic Square
Index entries for sequences related to magic squares


EXAMPLE

An illustration of the unique square of order 3:
++
 2  7  6 
++
 9  5  1 
++
 4  3  8 
++


CROSSREFS

Sequence in context: A118799 A206341 A024393 * A105976 A137064 A092675
Adjacent sequences: A006049 A006050 A006051 * A006053 A006054 A006055


KEYWORD

nonn,hard,nice,more


AUTHOR

N. J. A. Sloane.


STATUS

approved



