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A278970
Partition an n X n square into multiple non-congruent integer-sided rectangles. a(n) is ceiling(n/log(n)) + 3 - the least possible difference between the largest and smallest area.
3
4, 2, 3, 2, 2, 1, 2, 0, 2, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2, 3, 2, 1, 2, 2, 3, 3, 1, 2, 3, 1, 1, 2, 2, 3, 4, 3, 2, 2, 3, 3, 3, 2, 3, 4, 2, 4, 3, 2, 4, 3, 2, 3, 3, 3, 3, 4, 3, 3, 5, 4, 4, 4
OFFSET
3,1
COMMENTS
If ceiling(n/log(n)) + 3 is an upper bound for the Mondrian Art Problem (A276523), a(n) is the amount by which the optimal value beats the upper bound.
Terms a(86) and a(139) are at least 5. Term a(280) is at least 7.
Term a(138) is at least 9, defect 22 (1200-1178) with 16 rectangles.
Best values known for a(66) to a(96): 3, 1, 1, 2, 1, 2, 0, 1, 1, 1, 2, 1, 0, 1, 2, 1, 2, 2, 1, 1, 5, 1, 3, 1, 0, 1, 2, 2, 0, 0, 1.
CROSSREFS
Sequence in context: A333215 A028947 A068152 * A182199 A217435 A238352
KEYWORD
nonn,hard,more
AUTHOR
Ed Pegg Jr, Dec 02 2016
EXTENSIONS
a(45)-a(57) from Robert Gerbicz added/corrected, updated best known values to a(96), Ed Pegg Jr, Dec 28 2016
a(58)-a(65) from Michel Gaillard added by Ed Pegg Jr, Sep 02 2021
STATUS
approved