cp's OEIS Frontend

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.

%I A279848 #23 Jan 02 2017 19:54:36
%S A279848 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,
%T A279848 3,3,3,3,4,4,4,4,3
%N 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.
%C A279848 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.
%C A279848 Terms a(3) to a(45) verified optimal by R. Gerbicz.
%C A279848 Term a(103) is at least 9, defect 14 (630-616) with 17 rectangles.
%C A279848 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.
%H A279848 Mersenneforum.org puzzles, <a href="http://mersenneforum.org/showthread.php?t=21775">Mondrian art puzzles</a>.
%H A279848 Ed Pegg Jr, <a href="http://demonstrations.wolfram.com/MondrianArtProblem/">Mondrian Art Problem</a>.
%H A279848 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 A279848 Cf. A278970, A276523, A279596.
%K A279848 hard,more,nonn
%O A279848 3,7
%A A279848 _Ed Pegg Jr_, Dec 21 2016
%E A279848 a(28)-a(45) from _Robert Gerbicz_, Jan 01 2017