cp's OEIS Frontend

A006983 Number of simple perfect squared squares of order n up to symmetry.

%I A006983 M4482 #177 Mar 13 2025 09:45:49
%S A006983 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,8,12,26,160,441,1152,3001,
%T A006983 7901,20566,54541,144161,378197,990981,2578081,6674067,17086918
%N A006983 Number of simple perfect squared squares of order n up to symmetry.
%C A006983 A squared rectangle (which may be a square) is a rectangle dissected into a finite number of two or more squares. If no two squares have the same size, the squared rectangle is perfect. A squared rectangle is simple if it does not contain a smaller squared rectangle. The order of a squared rectangle is the number of constituent squares. - _Geoffrey H. Morley_, Oct 17 2012
%D A006983 J.-P. Delahaye, Les inattendus mathématiques, Belin-Pour la Science, Paris, 2004, pp. 95-96.
%D A006983 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006983 Stuart E. Anderson, <a href="http://www.squaring.net">Perfect Squared Rectangles and Squared Squares</a>
%H A006983 Stuart E. Anderson, <a href="/A006983/a006983.txt">Simple perfect squared squares in orders 27 to 37 - methods used and people involved. </a>
%H A006983 C. J. Bouwkamp, <a href="http://dx.doi.org/10.1016/0012-365X(92)90531-J">On some new simple perfect squared squares</a>, Discrete Math. 106-107 (1992) 67-75.
%H A006983 C. J. Bouwkamp and A. J. W. Duijvestijn, <a href="http://alexandria.tue.nl/repository/books/391207.pdf">Catalogue of Simple Perfect Squared Squares of orders 21 through 25</a>, EUT Report 92-WSK-03, Eindhoven University of Technology, Eindhoven, The Netherlands, November 1992.
%H A006983 C. J. Bouwkamp and A. J. W. Duijvestijn, <a href="http://alexandria.tue.nl/repository/books/430534.pdf">Album of Simple Perfect Squared Squares of order 26</a>, EUT Report 94-WSK-02, Eindhoven University of Technology, Eindhoven, The Netherlands, December 1994.
%H A006983 C. J. Bouwkamp, A. J. W. Duijvestijn, & N. J. A. Sloane, <a href="/A000162/a000162.pdf">Correspondence, 1971</a>.
%H A006983 G. Brinkmann and B. D. McKay, <a href="http://users.cecs.anu.edu.au/~bdm/papers/plantri-full.pdf">Fast generation of planar graphs</a>, MATCH Commun. Math. Comput. Chem., 58 (2007), 323-357.
%H A006983 Gunnar Brinkmann and Brendan McKay, <a href="http://users.cecs.anu.edu.au/~bdm/plantri/">plantri and fullgen</a> programs for generation of certain types of planar graph.
%H A006983 Gunnar Brinkmann and Brendan McKay, <a href="/A000103/a000103_1.pdf">plantri and fullgen</a> programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
%H A006983 A. J. W. Duijvestijn, <a href="/A006983/a006983.jpg">Illustration for a(21)=1</a> (The unique simple squared square of order 21. Reproduced with permission of the discoverer.)
%H A006983 A. J. W. Duijvestijn, <a href="http://doc.utwente.nl/17948/1/Duijvestijn93simple.pdf">Simple perfect squared squares and 2x1 squared rectangles of orders 21 to 24</a>, J. Combin. Theory Ser. B 59 (1993), 26-34.
%H A006983 A. J. W. Duijvestijn, Simple perfect squared squares and 2x1 squared rectangles of order 25, Math. Comp. 62 (1994), 325-332. <a href="http://dx.doi.org/10.1090/S0025-5718-1994-1208220-9">doi:10.1090/S0025-5718-1994-1208220-9</a>
%H A006983 A. J. W. Duijvestijn, Simple perfect squares and 2x1 squared rectangles of order 26, Math. Comp. 65 (1996), 1359-1364. <a href="http://dx.doi.org/10.1090/S0025-5718-96-00705-3">doi:10.1090/S0025-5718-96-00705-3</a> [<a href="http://www.squaring.net/downloads/TableI">TableI List of Simple Perfect Squared Squares of order 26</a> and <a href="http://www.squaring.net/downloads/TableII">TableII List of Simple Perfect Squared 2x1 Rectangles of order 26</a> are now on squaring.net and no longer located as described in the paper.]
%H A006983 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. 25.
%H A006983 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 A006983 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectSquareDissection.html">Perfect Square Dissection</a>
%H A006983 <a href="/index/Sq#squared_squares">Index entries for squared squares</a>
%Y A006983 Cf. A002962, A002881, A002839, A014530.
%Y A006983 Cf. A181340, A181735, A217155, A217156.
%Y A006983 Cf. A129947, A217149, A228953 (related to sizes of the squares).
%Y A006983 Cf. A349205, A349206, A349207, A349208, A349209, A349210 (related to ratios of element and square sizes).
%K A006983 nonn,hard,more,nice
%O A006983 1,22
%A A006983 _N. J. A. Sloane_
%E A006983 Leading term changed from 0 to 1, Apr 15 1996
%E A006983 More terms from _Stuart E Anderson_, May 08 2003, Nov 2010
%E A006983 Leading term changed back to 0, Dec 25 2010 (cf. A178688)
%E A006983 a(29) added by _Stuart E Anderson_, Aug 22 2010; contributors to a(29) include _Ed Pegg Jr_ and Stephen Johnson
%E A006983 a(29) changed to 7901, identified a duplicate tiling in order 29. - _Stuart E Anderson_, Jan 07 2012
%E A006983 a(28) changed to 3000, identified a duplicate tiling in order 28. - _Stuart E Anderson_, Jan 14 2012
%E A006983 a(28) changed back to 3001 after a complete recount of order 28 SPSS recalculated from c-nets with cleansed data, established the correct total of 3001. - _Stuart E Anderson_, Jan 24 2012
%E A006983 Definition clarified by _Geoffrey H. Morley_, Oct 17 2012
%E A006983 a(30) added by _Stuart E Anderson_, Apr 10 2013
%E A006983 a(31), a(32) added by _Stuart E Anderson_, Sep 29 2013
%E A006983 a(33), a(34) and a(35) added by _Stuart E Anderson_, May 02 2016
%E A006983 Moved comments on orders 27 to 35 to a linked file.  _Stuart E Anderson_, May 02 2016
%E A006983 a(36) and a(37) enumerated by Jim Williams, added by _Stuart E Anderson_, Jul 26 2020.