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 A279848 Partition an n X n square into multiple integer-sided rectangles where no one is a translation of any other. a(n) is ceiling(n/log(n)) - the least possible difference between the largest and smallest area. 1
 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 4, 4, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,7 COMMENTS If ceiling(n/log(n)) is an upper bound for the Mondrian Art Problem variant (A279596), a(n) is the amount by which the optimal value beats the upper bound. Terms a(3) to a(45) verified optimal by R. Gerbicz. Term a(103) is at least 9, defect 14 (630-616) with 17 rectangles. Best values known for a(46) to a(96): 3, 1, 2, 1, 1, 5, 2, 2, 1, 2, 2, 1, 1, 0, 3, 0, 2, 1, 2, 0, 0, 1, 1, 1, 1, 0, 1, 1, 4, 1, 0, 2, 0, 3, 1, 4, 3, 1, 1, 4, 2, 3, 1, 0, 4, 4, 0, 1, 1, 0, 0. LINKS Mersenneforum.org puzzles, Mondrian art puzzles. Ed Pegg Jr, Mondrian Art Problem. Ed Pegg Jr, Mondrian Art Problem Upper Bound for defect. CROSSREFS Cf. A278970, A276523, A279596. Sequence in context: A294874 A318324 A317934 * A001826 A003641 A165190 Adjacent sequences:  A279845 A279846 A279847 * A279849 A279850 A279851 KEYWORD hard,more,nonn AUTHOR Ed Pegg Jr, Dec 21 2016 EXTENSIONS a(28)-a(45) from Robert Gerbicz, Jan 01 2017 STATUS approved

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Last modified June 19 19:03 EDT 2019. Contains 324222 sequences. (Running on oeis4.)