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A261798 Maximum water retention of an associative magic square of order n. 2
0, 0, 0, 15, 59, 0, 361, 704, 1247, 0 (list; graph; refs; listen; history; text; internal format)
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.
(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.
Cf. A201126 (water retention on magic squares), A201127 (water retention on semi-magic squares), A261347 (water retention on number squares).
Sequence in context: A183942 A012691 A020187 * A022287 A288747 A223344
Craig Knecht, Sep 01 2015

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Last modified October 1 18:33 EDT 2023. Contains 365828 sequences. (Running on oeis4.)