%I #11 Jun 10 2019 22:17:59
%S 0,0,0,0,0,0,0,0,0,0,0,0,4,48,264,1256,5396,22540,92060,370788
%N Number of nontrivially compound perfect squared rectangles of order n up to symmetries of the rectangle.
%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.
%C A squared rectangle is simple if it does not contain a smaller squared rectangle, compound if it does, and trivially compound if a constituent square has the same side length as a side of the squared rectangle under consideration.
%H I. Gambini, <a href="http://alain.colmerauer.free.fr/alcol/ArchivesPublications/Gambini/carres.pdf">Quant aux carrés carrelés</a>, Thesis, Université de la Méditerranée Aix-Marseille II, 1999, p. 24. [Number of compound rectangles includes any that comprises a square sandwiched between two rectangles (from order 19) and excludes squares in separate column (order 24).]
%H <a href="/index/Sq#squared_rectangles">Index entries for squared rectangles</a>
%H <a href="/index/Sq#squared_squares">Index entries for squared squares</a>
%Y Cf. A217152 (counts symmetries of squared subrectangles as equivalent).
%Y Cf. A002839, A181340, A217154, A217155.
%K nonn,hard,more
%O 1,13
%A _Geoffrey H. Morley_, Sep 27 2012
%E a(19) and a(20) corrected (thanks to _Stuart E Anderson_'s computations which show I misinterpreted Gambini's counts) by _Geoffrey H. Morley_, Oct 12 2012