cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A261798 Maximum water retention of an associative magic square of order n.

This page as a plain text file.
%I A261798 #44 Mar 19 2019 18:08:39
%S A261798 0,0,0,15,59,0,361,704,1247,0
%N A261798 Maximum water retention of an associative magic square of order n.
%C A261798 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.
%C A261798 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.
%C A261798 a(11) >= 3226, a(12) >= 4840, a(13) >= 6972.
%C A261798 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.
%H A261798 Craig Knecht, <a href="/A261798/a261798_1.png">Order 5 associative magic square.</a>
%H A261798 Craig Knecht, <a href="/A261798/a261798_3.jpg">Order 7 associative magic square.</a>
%H A261798 Craig Knecht, <a href="/A261798/a261798_1.jpg">Order 8 associative magic square.</a>
%H A261798 Craig Knecht, <a href="/A261798/a261798_4.jpg">Order 9 associative magic square.</a>
%H A261798 Craig Knecht, <a href="/A261798/a261798_5.jpg">Order 12 associative magic square.</a>
%H A261798 Johan Ofverstedt, <a href="http://uu.diva-portal.org/smash/record.jsf?pid=diva2%3A534020">Water Retention on Magic Squares with Constraint Based Local Search</a>.
%H A261798 Wikipedia, <a href="https://commons.wikimedia.org/wiki/Category:Associative_magic_squares_of_order_4">Listing by water retention capacity.</a> and <a href="http://en.wikipedia.org/wiki/Water_retention_on_mathematical_surfaces">Water retention on mathematical surfaces</a>.
%e A261798 (16  3  2  13)
%e A261798 (5  10 11   8)
%e A261798 (9   6  7  12)
%e A261798 (4  15  14  1)
%e A261798 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.
%Y A261798 Cf. A201126 (water retention on magic squares), A201127 (water retention on semi-magic squares), A261347 (water retention on number squares).
%K A261798 nonn,more
%O A261798 1,4
%A A261798 _Craig Knecht_, Sep 01 2015