

A278970


Partition an n X n square into multiple noncongruent integersided rectangles. a(n) is ceiling(n/log(n)) + 3  the least possible difference between the largest and smallest area.


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 (12001178) with 16 rectangles.
Best values known for a(58) to a(96): 2, 3, 0, 3, 3, 1, 4, 1, 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..57.
Ed Pegg Jr, Mondrian Art Problem Upper Bound for defect


CROSSREFS

Cf. A276523, A279596.
Sequence in context: A018845 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

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


STATUS

approved



