cp's OEIS Frontend

A319589 A 3 X 3 magic square with five square entries, read by rows.

%I A319589 #15 Dec 17 2018 18:41:49
%S A319589 34969,83521,7585,14641,42025,69409,76465,529,49081
%N A319589 A 3 X 3 magic square with five square entries, read by rows.
%C A319589 Some magic squares of order 3 with five square entries have this parametric form:
%C A319589 |-----------------------|-----------------------|-----------------------|
%C A319589 |        (x*y)^2        |          y^4          |sqrt(z)*(3*x^2 - y^2)/2|
%C A319589 |-----------------------|-----------------------|-----------------------|
%C A319589 |          x^4          |           z           |       2*z - x^4       |
%C A319589 |-----------------------|-----------------------|-----------------------|
%C A319589 |sqrt(z)*(3*y^2 - x^2)/2|       2*z - y^4       |     2*z - (x*y)^2     |
%C A319589 |-----------------------|-----------------------|-----------------------|
%C A319589 where z = (x^2 + y^2)^2/4, x and y are integers such that (x^4 - y^4 + 2*(x*y)^2)/2 is a square (e.g., x = 11 and y = 17; x = 5337 and y = 6257).
%C A319589 This sequence presents the magic square belonging to this family and having the smallest possible magic sum (S = 126075).
%H A319589 <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>
%e A319589 The magic square is
%e A319589 +-------+-------+-------+
%e A319589 | 187^2 |  17^4 |  7585 |
%e A319589 +-------+-------+-------+
%e A319589 |  11^4 | 205^2 | 69409 |
%e A319589 +-------+-------+-------+
%e A319589 | 76465 |  23^2 | 49081 |
%e A319589 +-------+-------+-------+
%Y A319589 Cf. A221669, A268855.
%K A319589 nonn,fini,full,tabf
%O A319589 1,1
%A A319589 _Arkadiusz Wesolowski_, Sep 23 2018