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%I #22 Oct 27 2020 08:44:08
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,112,192,332,479,661,825,1179,
%T 1544,2134,2710,3641,4988,6391,8430,11216,15039,20242
%N Largest possible side length for a perfect squared square of order n; or 0 if no such square exists.
%C A squared rectangle (which may be a square) is a rectangle dissected into a finite number, two or more, of squares. If no two of these squares have the same size the squared rectangle is perfect. The order of a squared rectangle is the number of constituent squares. By convention the sides of the subsquares are integers with no common factor.
%C A squared rectangle is simple if it does not contain a smaller squared rectangle. Every perfect square with the largest known side length for each order up to 37 is simple.
%H S. E. Anderson, <a href="http://www.squaring.net/">Perfect Squared Rectangles and Squared Squares</a>.
%H Stuart Anderson, <a href="http://www.squaring.net/sq/ss/s-pss.html">'Special' Perfect Squared Squares"</a>, accessed 2014. - _N. J. A. Sloane_, Mar 30 2014
%H Ed Pegg Jr., <a href="https://community.wolfram.com/groups/-/m/t/2044450">Advances in Squared Squares</a>, Wolfram Community Bulletin, Jul 23 2020
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectSquareDissection.html">Perfect Square Dissection</a>
%Y Cf. A006983, A089047, A129947, A181735, A217148, A217156.
%K nonn,hard,more
%O 1,21
%A _Geoffrey H. Morley_, Sep 27 2012
%E a(29) from _Stuart E Anderson_ added by _Geoffrey H. Morley_, Nov 23 2012
%E a(30), a(31), a(32) from Lorenz Milla and _Stuart E Anderson_, added by _Stuart E Anderson_, Oct 05 2013
%E For additional terms see the Ed Pegg link, also A006983. - _N. J. A. Sloane_, Jul 29 2020
%E a(33) to a(37) from J. B. Williams added by _Stuart E Anderson_, Oct 27 2020
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