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, 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

Offset: 3

Author

Ed Pegg Jr, Dec 21 2016

Keywords

• hard
• more
• nonn

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.

Extensions

a(28)-a(45) from Robert Gerbicz, Jan 01 2017