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A060655
Pack n integer-sided rectangles into the smallest possible square so that no sides of the rectangle are the same. Sequence gives the side of the smallest square.
1
2, 4, 6, 8, 11, 14, 18, 21, 24, 28, 32, 37, 41, 46, 51, 55, 60
OFFSET
1,1
COMMENTS
Those terms that are > ceiling(sqrt(n*(n+1)*(2n+1)/3)) are only the best currently known solutions. - Larry Reeves (larryr(AT)acm.org), Apr 19 2001
a(1)-a(17) except a(15) are known to be the smallest possible. - Sean A. Irvine, Dec 13 2022
LINKS
Sean A. Irvine, Java program (github)
Sean A. Irvine, Solution for a(16)
Sean A. Irvine, Solution for a(17)
FORMULA
a(n) >= sqrt(n*(n+1)*(2n+1)/3).
CROSSREFS
Sequence in context: A212555 A328787 A339573 * A117490 A359275 A032514
KEYWORD
nonn,hard,more
AUTHOR
Jason Earls, Apr 18 2001
EXTENSIONS
Data updated from values at Friedman link by Sean A. Irvine, Dec 05 2022
a(16) from Sean A. Irvine, Dec 13 2022
a(17) from Sean A. Irvine, Dec 17 2022
STATUS
approved