A271652 - OEIS

%I #36 Jan 20 2020 10:51:37

%S 1,9,432,3600,907200

%N Number of n X n number squares where all (n-1)^2 2 X 2 subset diagonals have the same sum though those sums may differ.

%C A number square contains all numbers from 1 to n^2 without duplicates.

%C The 2 X 2 subset diagonal sums in these squares are equal, though those sums may differ.

%C When the single unit 2 X 2 subset is required to have diagonals with equal sums every rectangle within the generated square will have diagonals with equal sums.

%C Reversible squares are a previously defined entity. They require all symmetrically opposite pairs in each row and column to have the same sum in addition to the diagonal constraints noted above.

%C It is an embarrassment that no one has enumerated the order 6 magic squares. Richard C. Schroeppel provided the exact count for the order 5 magic squares in 1973 - now more than 40 years ago.

%H Craig Knecht, <a href="/A271652/a271652.txt">F1 code and order 3 examples.</a>

%H Craig Knecht, <a href="/A271652/a271652_1.txt">F1 code for the 48 Order 4 reversible squares.</a>

%H Craig Knecht, <a href="/A271652/a271652_4.txt">F1 code for the 907,200 order 6 examples.</a>

%H Craig Knecht, <a href="/A271652/a271652_2.png">Reversible square.</a>

%H Harry White, <a href="http://budshaw.ca/Reversible.html">Reversible squares.</a>

%e 3 X 3 square where all four 2 X 2 subset diagonals have the same sum, though those sums may differ:

%e 1 3 2    (1 + 9 = 7 + 3)  (3 + 8 = 9 + 2)

%e 7 9 8    (7 + 6 = 4 + 9)  (9 + 5 = 6 + 8)

%e 4 6 5

%Y Cf. A270205 (reversible cube).

%K nonn

%O 1,2

%A _Craig Knecht_, Apr 11 2016