This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A217154 #8 Oct 13 2012 04:01:49 %S A217154 0,0,0,0,0,0,0,0,2,14,62,235,821,2868,10193,36404,130174,466913, %T A217154 1681999,6083873 %N A217154 Number of perfect squared rectangles of order n up to symmetries of the rectangle. %C A217154 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. %C A217154 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. %D A217154 See crossrefs for references and links. %H A217154 <a href="/index/Sq#squared_rectangles">Index entries for squared rectangles</a> %H A217154 <a href="/index/Sq#squared_squares">Index entries for squared squares</a> %F A217154 a(n) = A002839(n) + A217153(n) + A217375(n). %F A217154 a(n) >= 2*a(n-1) + A002839(n) + 2*A002839(n-1) + A217153(n) + 2*A217153(n-1), with equality for n<19. %e A217154 a(10) = 14 comprises the A002839(10) = 6 simple perfect squared rectangles (SPSRs) of order 10 and the 8 trivially compound perfect squared rectangles which each comprises one of the two order 9 SPSRs and one other square. %Y A217154 Cf. A110148 (counts symmetries of any squared subrectangles as equivalent). %Y A217154 Cf. A181735, A217156. %K A217154 nonn,hard,more %O A217154 1,9 %A A217154 _Geoffrey H. Morley_, Sep 27 2012 %E A217154 a(19) and a(20) corrected by _Geoffrey H. Morley_, Oct 12 2012