OFFSET
3,1
COMMENTS
Similar to the Mondrian Art sequence (A276523), but allowing repetition of rectangles with different orientations.
Proved optimal to a(45) by R. Gerbicz. Best values known for a(46)-a(96): 10, 12, 11, 12, 12, 8, 12, 12, 13, 12, 12, 14, 14, 15, 12, 15, 14, 15, 14, 16, 16, 15, 16, 16, 16, 17, 16, 17, 14, 17, 18, 16, 18, 16, 18, 15, 16, 18, 18, 16, 18, 17, 19, 20, 17, 17, 21, 20, 20, 21, 22.
Seems to be bounded above by ceiling(n/log(n)). The currently verified distances from this bound are 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 (A279848).
LINKS
Robert Gerbicz, Optimal tilings for n = 3..45
Mersenneforum.org puzzles, Mondrian art puzzles.
Ed Pegg Jr, Mondrian Art Problem.
Ed Pegg Jr, Mondrian Art Problem Upper Bound for defect.
EXAMPLE
The 9 X 9 square can be divided into non-translatable rectangles with
aaaaaaaab
ddddddeeb
fggghheeb
fggghheeb
fiiihheeb
fiiijjjjb
fiiijjjjb
fkkkkkkkb
ccccccccc
CROSSREFS
KEYWORD
hard,more,nonn
AUTHOR
Ed Pegg Jr, Dec 15 2016
EXTENSIONS
Moved terms to A279848, expanded best values known
a(28)-a(45) from Robert Gerbicz, Jan 01 2017
STATUS
approved