A278970 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.

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, 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

Offset: 3

Author

Ed Pegg Jr, Dec 02 2016

Keywords

• nonn
• hard
• more

Comments

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.

Terms a(86) and a(139) are at least 5. Term a(280) is at least 7.

Term a(138) is at least 9, defect 22 (1200-1178) with 16 rectangles.

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.

Links

• Ed Pegg Jr, Mondrian Art Problem Upper Bound for defect

Crossrefs

Cf. A276523, A279596.

Extensions

a(45)-a(57) from Robert Gerbicz added/corrected, updated best known values to a(96), Ed Pegg Jr, Dec 28 2016

a(58)-a(65) from Michel Gaillard added by Ed Pegg Jr, Sep 02 2021