cp's OEIS Frontend

A217374 Number of trivially compound perfect squared rectangles of order n up to symmetries of the rectangle and its subrectangles.

%I A217374 #12 Oct 13 2012 04:01:32
%S A217374 0,0,0,0,0,0,0,0,0,4,16,60,194,622,2128,7438,25852,90266,317350,
%T A217374 1127800
%N A217374 Number of trivially compound perfect squared rectangles of order n up to symmetries of the rectangle and its subrectangles.
%C A217374 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 A217374 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 A217374 C. J. Bouwkamp, On the dissection of rectangles into squares (Papers I-III), Koninklijke Nederlandsche Akademie van Wetenschappen, Proc., Ser. A, <a href="http://www.dwc.knaw.nl/DL/publications/PU00018283.pdf">Paper I</a>, 49 (1946), 1176-1188 (=Indagationes Math., v. 8 (1946), 724-736); <a href="http://www.dwc.knaw.nl/DL/publications/PU00018294.pdf">Paper II</a>, 50 (1947), 58-71 (=Indagationes Math., v. 9 (1947), 43-56); <a href="http://www.dwc.knaw.nl/DL/publications/PU00018295.pdf">Paper III</a>, 50 (1947), 72-78 (=Indagationes Math., v. 9 (1947), 57-63). [Paper I has terms up to a(13) on p. 1178.]
%H A217374 C. J. Bouwkamp, <a href="http://www.dwc.knaw.nl/DL/publications/PU00018444.pdf">On the construction of simple perfect squared squares</a>, Koninklijke Nederlandsche Akademie van Wetenschappen, Proc., Ser. A, 50 (1947), 1296-1299 (=Indagationes Math., v. 9 (1947), 622-625).
%H A217374 <a href="/index/Sq#squared_rectangles">Index entries for squared rectangles</a>
%F A217374 a(n) = a(n-1) + 2*A002839(n-1) + 2*A217152(n-1).
%Y A217374 Cf. A217375 (counts symmetries of squared subrectangles as distinct).
%Y A217374 Cf. A110148.
%K A217374 nonn,hard,more
%O A217374 1,10
%A A217374 _Geoffrey H. Morley_, Oct 02 2012
%E A217374 a(20) corrected by _Geoffrey H. Morley_, Oct 12 2012