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A081287 - OEIS
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A081287
Excess area when consecutive squares of sizes 1 to n are packed into the smallest possible rectangle.
4
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
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
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.
FORMULA
a(n) = A038666(n) - A000330(n). - Pontus von Brömssen, Mar 01 2024
EXAMPLE
Verified best rectangles > 5 are as follows:
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
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