

A261798


Maximum water retention of an associative magic square of order n.


2




OFFSET

1,4


COMMENTS

Two of the most famous magic squares are associative magic squares  the Lo Shu magic square and Dürer's magic square. Al Zimmermann's programming contest in 2010 produced the presently known maximum retention values for magic squares order 4 to 28 A201126. No concerted effort has been made to find the maximum retention for associative magic squares.
There are 4211744 different water retention patterns for a 7 x 7 square A054247 and 1.12*10^18 different order 7 associative magic squares. There is no proof that the presently stated maximum retention values greater than order 5 are actually the maximum possible retention.
a(11) >= 3226, a(12) >= 4840, a(13) >= 6972.
The Wikipedia link below shows the first attempt to classify a set of data by its water retention. Here the 48 associative order 4 magic squares are thus classified. Perhaps there might be some correlation between this surface evaluation and Mohs hardness scale.


LINKS



EXAMPLE

(16 3 2 13)
(5 10 11 8)
(9 6 7 12)
(4 15 14 1)
This is Albrecht Dürer's famous magic square in Melancholia I. Dürer put the date of its creation (1514) in the numbers in the bottom row. This square holds 5 units of water.


CROSSREFS

Cf. A201126 (water retention on magic squares), A201127 (water retention on semimagic squares), A261347 (water retention on number squares).


KEYWORD

nonn,more


AUTHOR



STATUS

approved



