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%I #33 Sep 02 2021 17:36:56
%S 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,
%T 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
%N 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.
%C 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.
%C Terms a(86) and a(139) are at least 5. Term a(280) is at least 7.
%C Term a(138) is at least 9, defect 22 (1200-1178) with 16 rectangles.
%C 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.
%H Ed Pegg Jr, <a href="http://math.stackexchange.com/questions/2041189/mondrian-art-problem-upper-bound-for-defect">Mondrian Art Problem Upper Bound for defect</a>
%Y Cf. A276523, A279596.
%K nonn,hard,more
%O 3,1
%A _Ed Pegg Jr_, Dec 02 2016
%E a(45)-a(57) from _Robert Gerbicz_ added/corrected, updated best known values to a(96), _Ed Pegg Jr_, Dec 28 2016
%E a(58)-a(65) from _Michel Gaillard_ added by _Ed Pegg Jr_, Sep 02 2021
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