cp's OEIS Frontend

A271652 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.

%I A271652 #36 Jan 20 2020 10:51:37
%S A271652 1,9,432,3600,907200
%N A271652 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 A271652 A number square contains all numbers from 1 to n^2 without duplicates.
%C A271652 The 2 X 2 subset diagonal sums in these squares are equal, though those sums may differ.
%C A271652 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 A271652 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 A271652 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 A271652 Craig Knecht, <a href="/A271652/a271652.txt">F1 code and order 3 examples.</a>
%H A271652 Craig Knecht, <a href="/A271652/a271652_1.txt">F1 code for the 48 Order 4 reversible squares.</a>
%H A271652 Craig Knecht, <a href="/A271652/a271652_4.txt">F1 code for the 907,200 order 6 examples.</a>
%H A271652 Craig Knecht, <a href="/A271652/a271652_2.png">Reversible square.</a>
%H A271652 Harry White, <a href="http://budshaw.ca/Reversible.html">Reversible squares.</a>
%e A271652 3 X 3 square where all four 2 X 2 subset diagonals have the same sum, though those sums may differ:
%e A271652 1 3 2    (1 + 9 = 7 + 3)  (3 + 8 = 9 + 2)
%e A271652 7 9 8    (7 + 6 = 4 + 9)  (9 + 5 = 6 + 8)
%e A271652 4 6 5
%Y A271652 Cf. A270205 (reversible cube).
%K A271652 nonn
%O A271652 1,2
%A A271652 _Craig Knecht_, Apr 11 2016