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 A081287 Excess area when consecutive squares of sizes 1 to n are packed into the smallest possible rectangle. 3
 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, 26, 35, 31, 31, 34, 35 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Restricted to packings with the squares aligned with the sides of the rectangle. REFERENCES R. K. Guy, Unsolved Problems in Geometry, Section D4, has information about several related problems. R. M. Kurchan (editor), Puzzle Fun, Number 18 (December 1997), pp. 9-10. LINKS Jean-François Alcover, Mathematica script (after E. Pegg and R. Korf) R. Ellard and Des MacHale, Packing Squares into Rectangles, The Mathematical Gazette, Vol. 96, No. 535 (March 2012), 1-18. Eric Huang and Richard E. Korf, New improvements in optimal rectangle packing Richard E. Korf, Optimal Rectangle Packing: New Results, ICAPS, 2004. Ed Pegg Jr, Packing squares E. Pegg and R. Korf, Tightly Packed Squares. EXAMPLE Verified best rectangles >5 are as follows (the dots are just to maintain the alignment): .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 -------------------------------------------------------------------------------------- .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 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 Visual representations are at the Tightly Packed Squares link. CROSSREFS Cf. A038666. Sequence in context: A107623 A218333 A212533 * A303715 A204188 A347682 Adjacent sequences:  A081284 A081285 A081286 * A081288 A081289 A081290 KEYWORD nice,nonn,more AUTHOR Ed Pegg Jr, Mar 16 2003 EXTENSIONS Four extra terms computed by Korf, May 24 2005 More terms from Ed Pegg Jr, Feb 14 2008 and again Sep 16 2009 STATUS approved

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Last modified January 28 06:43 EST 2022. Contains 350654 sequences. (Running on oeis4.)