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%I #12 Jun 24 2019 20:16:24
%S 0,0,0,0,0,0,0,0,0,8,40,168,604,2076,7320,26132,93352,333992,1199716,
%T 4329180
%N Number of trivially compound perfect squared rectangles of order n up to symmetries of the rectangle.
%C A squared rectangle 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. [A217153 up to a(18).]
%H <a href="/index/Sq#squared_rectangles">Index entries for squared rectangles</a>
%F a(n) >= 2*a(n-1) + 4*A002839(n-1) + 4*A217153(n-1), with equality for n<19.
%Y Cf. A217374 (counts symmetries of squared subrectangles as equivalent).
%Y Cf. A217154.
%K nonn,hard,more
%O 1,10
%A _Geoffrey H. Morley_, Oct 02 2012
%E a(20) corrected by _Geoffrey H. Morley_, Oct 12 2012