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A081287
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Excess area when consecutive squares of sizes 1 to n are packed into the smallest possible rectangle.
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3
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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)
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OFFSET
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1,4
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COMMENTS
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Restricted to packings with the squares aligned with the sides of the rectangle.
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=1..32.
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.
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EXAMPLE
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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
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.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.
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CROSSREFS
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Cf. A038666.
Sequence in context: A107623 A218333 A212533 * A303715 A204188 A347682
Adjacent sequences: A081284 A081285 A081286 * A081288 A081289 A081290
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KEYWORD
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nice,nonn,more
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AUTHOR
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Ed Pegg Jr, Mar 16 2003
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EXTENSIONS
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Four extra terms computed by Korf, May 24 2005
More terms from Ed Pegg Jr, Feb 14 2008 and again Sep 16 2009
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STATUS
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approved
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