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 A081287 #43 Aug 18 2025 14:15:12 %S A081287 0,1,1,5,5,8,14,6,15,20,7,17,17,20,25,16,9,30,21,20,33,27,28,28,22,29, %T A081287 26,35,31,31,34,35 %N A081287 Excess area when consecutive squares of sizes 1 to n are packed into the smallest possible rectangle. %C A081287 Restricted to packings with the squares aligned with the sides of the rectangle. %D A081287 R. K. Guy, Unsolved Problems in Geometry, Section D4, has information about several related problems. %D A081287 R. M. Kurchan (editor), Puzzle Fun, Number 18 (December 1997), pp. 9-10. %H A081287 Jean-François Alcover, <a href="/A081287/a081287.txt">Mathematica script (after E. Pegg and R. Korf)</a> %H A081287 R. Ellard and Des MacHale, <a href="https://doi.org/10.1017/S0025557200003922">Packing Squares into Rectangles</a>, The Mathematical Gazette, Vol. 96, No. 535 (March 2012), 1-18. %H A081287 Eric Huang and Richard E. Korf, <a href="http://search-conference.org/index.php/Main/SOCS09program?action=download&upname=SoCS09-13.pdf">New improvements in optimal rectangle packing</a> %H A081287 Richard E. Korf, <a href="https://icaps04.icaps-conference.org/icapspapers/ICAPS04KorfR.pdf">Optimal Rectangle Packing: New Results</a>, ICAPS, 2004. %H A081287 Ed Pegg Jr, <a href="https://www.mathpuzzle.com/MAA/06-Square%20Packing/mathgames_12_01_03.html">Square Packing</a> %H A081287 E. Pegg and R. Korf, <a href="http://demonstrations.wolfram.com/TightlyPackedSquares/">Tightly Packed Squares</a>. %F A081287 a(n) = A038666(n) - A000330(n). - _Pontus von Brömssen_, Mar 01 2024 %e A081287 Verified best rectangles > 5 are as follows: %e A081287 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 %e A081287 -------------------------------------------------------------------------------------- %e A081287 9 11 14 15 15 19 23 22 23 23 28 39 31 47 34 38 39 64 56 43 70 74 63 81 51 95 85 %e A081287 11 14 15 20 27 27 29 38 45 55 54 46 69 53 85 88 98 68 88 129 89 94 123 106 186 110 135 %e A081287 Visual representations are at the Tightly Packed Squares link. %Y A081287 Cf. A000330, A038666, A369891. %K A081287 nice,nonn,more %O A081287 1,4 %A A081287 _Ed Pegg Jr_, Mar 16 2003 %E A081287 Four extra terms computed by Korf, May 24 2005 %E A081287 More terms from _Ed Pegg Jr_, Feb 14 2008 and again Sep 16 2009