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

3,7

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

Table of n, a(n) 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.

Crossrefs

Cf. A278970, A276523, A279596.

Sequence in context: A318324 A317934 A353376 * A001826 A003641 A355241

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