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 A174386 #7 Aug 29 2012 03:36:25 %S A174386 0,0,0,0,0,0,49,98,121,196,128,196,289,242,441,441,484,722,722,1024, %T A174386 1156,1225 %N A174386 Smallest possible area for a perfect isosceles right triangled square of order n; or 0 if no such square exists. %C A174386 These terms are only conjectures, but are thought highly likely to be correct for n<18. %C A174386 A tiling is perfect if no two tiles are the same size. The order of a tiling is the number of tiles. An integer n is the order of a perfect isosceles right triangled square if and only if n>=7. %C A174386 We require the area of each triangular tile to be m^2 or m^2/2, where m is an integer. A tiling of an integer-sided square can often be scaled by the factor 1/sqrt(2) and still meet this requirement. %D A174386 J. D. Skinner II, C. A. B. Smith, and W. T. Tutte, On the Dissection of Rectangles into Right-Angled Isosceles Triangles, Journal of Combinatorial Theory, Series B 80 (2000), 277-319. %H A174386 S. E. Anderson, <a href="http://www.squaring.net/">Perfect Squared Rectangles, Squared Squares, and Isosceles Right Triangled Squares</a> %H A174386 S. E. Anderson, <a href="http://www.squaring.net/tri/twt.html">Tilings by Triangles</a> (see Morley's Isosceles Right Triangulation code (MIRT code)) %e A174386 Diagrams for the known tilings associated with the conjectured terms up to a(20) are in pdfs downloadable from Stuart Anderson's website. All squares are depicted with integer sides, but many can be scaled by the factor 1/sqrt(2). %e A174386 In MIRT code (see link for an explanation) one of the three known tilings for n=21, area 1156, is -162 114 66 127 126 -56 82 -113 102 -63 -83 35 34 -103 -57 90 91 -26 45 44 -25. %e A174386 The known tiling for n=22, area 1225, is -165 134 103 92 91 -76 -36 67 143 47 46 -52 -85 84 -23 75 -14 53 -120 121 -115 114. %e A174386 The tilings for a(11) and a(12) were found by J. D. Skinner and published in Skinner et al. (2000). G. H. Morley found the tilings for subsequent terms. %Y A174386 Cf. A129947. %K A174386 hard,more,nonn %O A174386 1,7 %A A174386 _Geoffrey H. Morley_, Mar 18 2010 %E A174386 XB code renamed MIRT code by _Geoffrey H. Morley_, May 12 2012