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

3,1

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

Table of n, a(n) for n=3..65.

Ed Pegg Jr, Mondrian Art Problem Upper Bound for defect

Crossrefs

Cf. A276523, A279596.

Sequence in context: A333215 A028947 A068152 * A182199 A217435 A238352

Adjacent sequences: A278967 A278968 A278969 * A278971 A278972 A278973

Keyword

nonn,hard,more

Author

Ed Pegg Jr, Dec 02 2016

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

Status

approved