login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A110148 Number of perfect squared rectangles of order n up to symmetries of the rectangle and of its subrectangles if any. 5

%I

%S 0,0,0,0,0,0,0,0,2,10,38,127,408,1375,4783,16645,58059,203808,722575

%N Number of perfect squared rectangles of order n up to symmetries of the rectangle and of its subrectangles if any.

%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. [_Geoffrey H. Morley_, Oct 12 2012]

%H 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(12) and an incorrect value for a(13) on p. 1178.]

%H 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). [Correct terms up to a(13) on p. 1299.]

%H I. M. Yaglom, <a href="http://ilib.mirror1.mccme.ru/djvu/yaglom/square.htm">How to dissect a square?</a> (in Russian), Nauka, Moscow, 1968. In djvu format (1.7M), also as this <a href="http://www.squaring.net/downloads/Yaglom-square.pdf">pdf</a> (9.5M). [Terms up to a(13) on pp. 26-7.]

%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>

%F a(n) = A002839(n) + A217152(n) + A217374(n). - _Geoffrey H. Morley_, Oct 12 2012

%F a(n) = a(n-1) + A002839(n) + A002839(n-1) + A217152(n) + A217152(n-1). - _Geoffrey H. Morley_, Oct 12 2012

%Y Cf. A217154 (counts symmetries of any subrectangles as distinct).

%Y Cf. A181735, A217153, A217156.

%K nonn,hard,more

%O 1,9

%A Tanya Khovanova, Feb 18 2007

%E Definition corrected and a(14)-a(19) added by _Geoffrey H. Morley_, Oct 12 2012

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 11 05:07 EST 2016. Contains 279034 sequences.