A103744 - OEIS

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A103744

There are, up to equivalence (i.e., symmetries and rotations), 880 magic squares of order 4 (cf. A006052). Say that two squares are of the same type if one can be obtained from the other by complementing (replacing each entry i with 17-i) and applying symmetries. There are 12 types. Sequence gives the population of each of the types, arranged in nondecreasing order.

%I #12 Nov 11 2019 09:23:15

%S 8,8,48,48,48,56,56,56,56,96,96,304

%N There are, up to equivalence (i.e., symmetries and rotations), 880 magic squares of order 4 (cf. A006052). Say that two squares are of the same type if one can be obtained from the other by complementing (replacing each entry i with 17-i) and applying symmetries. There are 12 types. Sequence gives the population of each of the types, arranged in nondecreasing order.

%D William H. Benson and Ostwald Jacoby, New Recreations with Magic Squares, Dover Publications, New York, 1976.

%D Rene Descombes, La magie du carré, Vuibert, 2004.

%D Henry E. Dudeney, Amusements in Mathematics, Dover Publications, New York.

%H Aale de Winkel, <a href="http://www.magichypercubes.com/Encyclopedia/DataBase/Squares_Order4.html">Squares of order 4</a>

%K nonn,fini,full

%O 1,1

%A _Philippe Deléham_, Mar 28 2005