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A006052
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Number of magic squares of order n composed of the numbers from 1 to n^2, counted up to rotations and reflections.
(Formerly M5482)
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40
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OFFSET
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1,4
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COMMENTS
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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
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REFERENCES
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E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Vol. II, pp. 778-783 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).
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LINKS
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EXAMPLE
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An illustration of the unique (up to rotations and reflections) magic square of order 3:
+---+---+---+
| 2 | 7 | 6 |
+---+---+---+
| 9 | 5 | 1 |
+---+---+---+
| 4 | 3 | 8 |
+---+---+---+
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CROSSREFS
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KEYWORD
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nonn,hard,nice,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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