cp's OEIS Frontend

A220164 Number of simple squared squares of order n up to symmetry.

%I A220164 #31 Feb 16 2025 08:33:18
%S A220164 0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,5,15,19,57,72,275,499,1778,3705,11318,
%T A220164 24525,65906,135599,333938,687969,1681759,3652677
%N A220164 Number of simple squared squares of order n up to symmetry.
%C A220164 A squared rectangle is a rectangle dissected into a finite number, two or more, of squares, called the elements of the dissection. If no two of these squares have the same size the squared rectangle is called perfect, otherwise it is imperfect. The order of a squared rectangle is the number of constituent squares. The case in which the squared rectangle is itself a square is called a squared square. The dissection is simple if it contains no smaller squared rectangle, otherwise it is compound. This sequence counts both perfect and imperfect simple squared squares up to symmetry.
%D A220164 See A006983 and A217156.
%H A220164 S. E. Anderson, <a href="http://www.squaring.net/sq/ss/spss/spss.html">Simple Perfect Squared Squares</a>
%H A220164 S. E. Anderson, <a href="http://www.squaring.net/sq/ss/siss/siss.html">Simple Imperfect Squared Squares</a>
%H A220164 S. E. Anderson, <a href="http://www.squaring.net/quilts/mrs-perkins-quilts.html">Mrs Perkins's Quilts</a>
%H A220164 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectSquareDissection.html">Perfect Square Dissection</a>
%F A220164 a(n) = A006983(n) + A002962(n).
%Y A220164 Cf. A006983, A002962, A217156, A089046.
%K A220164 nonn,hard
%O A220164 1,15
%A A220164 _Stuart E Anderson_, Dec 06 2012
%E A220164 a(13)-a(29) from _Stuart E Anderson_, Dec 07 2012
%E A220164 Clarified some definitions in comments and added a(30) - _Stuart E Anderson_, Jun 03 2013
%E A220164 a(31), a(32) added by _Stuart E Anderson_, Sep 30 2013